Class 10th Mathematics CBSE Solution
Exercise 8.1- In Fig. 8.13, find tan P - cot R. c p 12cm]
- If sin a = 3/4 calculate Cos A and tan A
- Given 15 cot A = 8, find sin A and sec A
- Given sec theta = 13/12 calculate all other trigonometric ratios
- If A and B are acute angles such that Cos A = Cos B, then show that A = B…
- If cottheta = 7/8 evaluate: (i) (1+sintegrate heta) (1-sintegrate…
- If 3 cot A = 4, check whether 1-tan^2a/1+tan^2a = cos^2a-sin^2a or not…
- In triangle ABC, right-angled at B, if tana = 1/root 3 find the value of: (i)…
- In PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values…
- State whether the following are true or false. Justify your answer. (i) The…
Exercise 8.2- Evaluate the following: (i) 60^circle cos30^circle +sin30^circle cos60^circle…
- Choose the correct option and justify your choice: 2tan30^circle
- 1-tan^245^circle /1+tan^245^circle = Choose the correct option and justify your…
- Sin 2A = 2 sin A is true when A = Choose the correct option and justify your…
- 2tan30^circle /1-tan^230^circle = Choose the correct option and justify your…
- If tan (a+b) = root 3 and tan (a-b) = 1/root 3 0^circle a+b less than equal to…
- State whether the following are true or false. Justify your answer (i) Sin (A +…
Exercise 8.3- Evaluate: (i) sin18^circle /cos72^circle (ii) tan26^circle /cot64^circle (iii)…
- Show that:(i) tan 48 tan 23 tan 42 tan 67 = 1(ii) cos 38 Cos 52 - sin 38 sin 52…
- If tan 2A = cot (A - 18), where 2A is an acute angle, find the value of A…
- If tan A = cot B, prove that A + B = 90
- If sec 4A = cosec (A - 20), where 4A is an acute angle, find the value of A…
- If A, B and C are interior angles of a triangle ABC, then show that sin (b+c/2)…
- Express sin 67 + Cos 75 in terms of trigonometric ratios of angles between 0 and…
Exercise 8.4- Express the trigonometric ratios sin A, sec A and tan A in terms of cot A…
- Write all the other trigonometric ratios of A in terms of sec A.
- Evaluate: (i) sin^263^circle + sin^227^circle /cos^217^circle + cos^273^circle…
- 9sec^2a-9tan^2a = Choose the correct option. Justify your choice.A. 1 B. 9 C. 8…
- (1+tantheta +sectheta) (1+cottheta -costheta c theta) = Choose the correct…
- Choose the correct option. Justify your choice.(Sec A + tan A) (1 - sin A) =A.…
- 1+tan^2a/1+cot^2a = Choose the correct option. Justify your choice.A. sec^2a B.…
- Prove the following identities, where the angles involved are acute angles for…
Testing
- In Fig. 8.13, find tan P - cot R. c p 12cm]
- If sin a = 3/4 calculate Cos A and tan A
- Given 15 cot A = 8, find sin A and sec A
- Given sec theta = 13/12 calculate all other trigonometric ratios
- If A and B are acute angles such that Cos A = Cos B, then show that A = B…
- If cottheta = 7/8 evaluate: (i) (1+sintegrate heta) (1-sintegrate…
- If 3 cot A = 4, check whether 1-tan^2a/1+tan^2a = cos^2a-sin^2a or not…
- In triangle ABC, right-angled at B, if tana = 1/root 3 find the value of: (i)…
- In PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values…
- State whether the following are true or false. Justify your answer. (i) The…
- Evaluate the following: (i) 60^circle cos30^circle +sin30^circle cos60^circle…
- Choose the correct option and justify your choice: 2tan30^circle
- 1-tan^245^circle /1+tan^245^circle = Choose the correct option and justify your…
- Sin 2A = 2 sin A is true when A = Choose the correct option and justify your…
- 2tan30^circle /1-tan^230^circle = Choose the correct option and justify your…
- If tan (a+b) = root 3 and tan (a-b) = 1/root 3 0^circle a+b less than equal to…
- State whether the following are true or false. Justify your answer (i) Sin (A +…
- Evaluate: (i) sin18^circle /cos72^circle (ii) tan26^circle /cot64^circle (iii)…
- Show that:(i) tan 48 tan 23 tan 42 tan 67 = 1(ii) cos 38 Cos 52 - sin 38 sin 52…
- If tan 2A = cot (A - 18), where 2A is an acute angle, find the value of A…
- If tan A = cot B, prove that A + B = 90
- If sec 4A = cosec (A - 20), where 4A is an acute angle, find the value of A…
- If A, B and C are interior angles of a triangle ABC, then show that sin (b+c/2)…
- Express sin 67 + Cos 75 in terms of trigonometric ratios of angles between 0 and…
- Express the trigonometric ratios sin A, sec A and tan A in terms of cot A…
- Write all the other trigonometric ratios of A in terms of sec A.
- Evaluate: (i) sin^263^circle + sin^227^circle /cos^217^circle + cos^273^circle…
- 9sec^2a-9tan^2a = Choose the correct option. Justify your choice.A. 1 B. 9 C. 8…
- (1+tantheta +sectheta) (1+cottheta -costheta c theta) = Choose the correct…
- Choose the correct option. Justify your choice.(Sec A + tan A) (1 - sin A) =A.…
- 1+tan^2a/1+cot^2a = Choose the correct option. Justify your choice.A. sec^2a B.…
- Prove the following identities, where the angles involved are acute angles for…
Exercise 8.1
Question 1.In Fig. 8.13, find tan P – cot R.
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)
Answer:Applying Pythagoras theorem for ΔPQR, we obtain
![](data:image/png;base64,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)
Pythagoras Theorem : the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
PR2 = PQ2 + QR2
(13)2 = (12)2 + QR2
169 cm2 = 144 cm2 + QR2
25 cm2 = QR2
QR = 5 cm
![](data:image/png;base64,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)
tan P = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAkCAMAAACzM5rVAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAA///b//+22///tv///9vb/9u2/9uQttv/kNv//7Zm27aQtrbbZrb/Zrbb25A6tpBmOpDbtmYAOma2AGa2kDoAZjoAOjpmADqQADpmZgAAOgA6OgAAAABmAAA6AAAADk3VUQAAAAF0Uk5TAEDm2GYAAACqSURBVHjaxZFRE4IgEIQXqJTKSINUMu///0uHA5XsqWaa9olbuBtuP+B7ietAvQakJ6K+DI7rSpjnDjCdEk2ngGOoiocGmpptCFcjWtJXOA0V+BAviyGN4hbpYw8XXB1cmiCcVeHZneimAEOjhqGaPxYGbSR925Ybb39Wny9Nb8IftEQ+M4hbC2czBjHyxmYM5shXBuDIx0vGYAlwZZCgZQxS5MgYvOgHDCbnAw9nkUqc7AAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAA///b//+22////9uQ29u2kNv//7Zm27ZmkLbbZrb/Zrbb25Bm25A6OpDbtmY6tmYAOma2OmZmkDo6AGa2kDoAAGaQZjoAZgA6ZgAAOgA6OgAAAAA6AAAAau0YfAAAAAF0Uk5TAEDm2GYAAAB0SURBVHjatZBJDoAwCEV/na3WWevE/a9pmtYoutKkfwMPWJAH/Ikioj25sXzs5fu+5aNo4zdirK6+T9he1ER7AS8hHviPqAdTYm2dlJ02HMw5MutUDaejlbOyik7OnFLHyqFophBA2gKptO6pQrCYKr8+ewD7GQd0VEiUHwAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
cot R = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAkCAMAAACzM5rVAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAA///b//+22///tv///9vb/9u2/9uQttv/kNv//7Zm27aQtrbbZrb/Zrbb25A6tpBmOpDbtmYAOma2AGa2kDoAZjoAOjpmADqQADpmZgAAOgA6OgAAAABmAAA6AAAADk3VUQAAAAF0Uk5TAEDm2GYAAACqSURBVHjaxZFRE4IgEIQXqJTKSINUMu///0uHA5XsqWaa9olbuBtuP+B7ietAvQakJ6K+DI7rSpjnDjCdEk2ngGOoiocGmpptCFcjWtJXOA0V+BAviyGN4hbpYw8XXB1cmiCcVeHZneimAEOjhqGaPxYGbSR925Ybb39Wny9Nb8IftEQ+M4hbC2czBjHyxmYM5shXBuDIx0vGYAlwZZCgZQxS5MgYvOgHDCbnAw9nkUqc7AAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAA///b//+22////9uQ29u2kNv//7Zm27ZmkLbbZrb/Zrbb25Bm25A6OpDbtmY6tmYAOma2OmZmkDo6AGa2kDoAAGaQZjoAZgA6ZgAAOgA6OgAAAAA6AAAAau0YfAAAAAF0Uk5TAEDm2GYAAAB0SURBVHjatZBJDoAwCEV/na3WWevE/a9pmtYoutKkfwMPWJAH/Ikioj25sXzs5fu+5aNo4zdirK6+T9he1ER7AS8hHviPqAdTYm2dlJ02HMw5MutUDaejlbOyik7OnFLHyqFophBA2gKptO6pQrCYKr8+ewD7GQd0VEiUHwAAAABJRU5ErkJggg==)
tan P - cot R = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAiCAMAAADF9REmAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAA///b//+22////9uQ29u2kNv//7Zm27ZmkLbbZrb/Zrbb25Bm25A6OpDbtmY6tmYAOma2OmZmkDo6AGa2kDoAAGaQZjoAZgA6ZgAAOgA6OgAAAAA6AAAAau0YfAAAAAF0Uk5TAEDm2GYAAACsSURBVHja7ZTJEsIwDEOVAm0JuAsEylL9/29yKO2AIQucOgO6aeY5zsESMHcJyT7/jBGb8K4N+6QZkm3C/xWzvMZ3acYcqujMI2P2eXSPZkxN9pvIjgTml8RnAQCayQ5H+Y756xuZ2gHAqgvkTjHbXecAZKc1Sl+PvDLixhxevN2jmcmLP6qaGX0ZqBHN3L2EmkcxpjkuABQtUPg6QTFCkhWyM0laf7fFmHnoBrm7EB6crXC4AAAAAElFTkSuQmCC)
= 0
tan P - cot R = 0
Question 2.If sin
calculate Cos A and tan A
Answer:Let ΔABC be a right-angled triangle, right-angled at point B
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Given that:
![](data:image/png;base64,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)
As we know trigonometrical ratios give ratio between sides of right angled triangle instead of their actual values. So from sin A we get the ratio of Perpendicular and Hypotenuse of the triangle. Now as we don't know the exact value let Perpendicular = 3 k and Hypotenuse = 4 k
According to Pythagoras theorem: (Hypotenuse)2 = (Base)2 + (Perpendicular)2
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(4k)2 = AB2 + (3k)2
16k2 - 9k2 = AB2
7k2 = AB2
![](data:image/png;base64,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)
Cos A = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,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)
And we know that
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASYAAAA3CAYAAAChOedQAAASsElEQVR4Xu3dB7AtS1UG4B8kqGQVRbICRjCg5OATRDIKPCWLCKIIkn1kVECygZwxPaKKiig5o2JEkvAAyclEzrm+qu6qfsPsvWfvs+8+e87trrp17z1npqd7Tfc/a/0r9GnSW5dAl0CXwJ5J4DR7Np4+nC6BLoEugXRgOvqL4AxJrp3km1ZM9V1JXpfkM0dfJBvP8BxJTkxyviRnTPKUJG/buLft33ihJNdJ8q1JTpvkoUk+tv3HHPseOzAdexkf9hMA09WSfFuSByT5liT3TvLhZmCnT3KFJNdI8sgkD0ny5cMe+B4+HzBdNcnPFZn+QJL3DMZ5liRPTPKGJA/a8RwA5k8k+Y0k35Dkx5N8bsdj2MrjOjBtRYyz6MSGeX2STyS5ZJIvjIz6RkmenuQeSR48i1kdziAfVzb9ZZJ8aTCEyyb5+yQPLwCx6xECpFcmeXeSm+764dt6XgembUly//v5sST/WsyPWy0Yri/ue5OckuTi3awblRLt8p+S/GOS245cwYT6nmLifeUQlsV3JnlLkl9P8qeH8PytPLID01bEOItOLFRm2g2TPGvBiL83yVuTfCDJxZJ8dBYz2+0gvzvJG5PcJMlf7fbRk57GbP+bJBctH5hJN+3bRR2Y9u2NHLvxWKxXSfKDSf5rwWNstpOTvKRwKYfxxT92EthOz/ilP0oyxi9t5wkH6wXhjSucLb9k+h2YDrYI5nL3FH7pdElelITJ56vLVBlrgM3CR6r+T5K/aHgW64nX6oJJ/rqYM7xXNvPZk/D8/V2Sr5aOXX/NJDS1FxfCmCnEi6gPGtszknzxgGN5bqM9/EiSKxWvGtMWCNfxDB+DrzG+Cyf5SOHfaJ1kNOSXzpvkekUuf5zk80sWB1PPtTygny1z/FRzvb6uX3431hdzjUnJ7G7bFH5pbE4+QGTQOjzWfZdb3QsdmLYqzr3tbBW/BAzunuSkJL+U5DkjM8E//X6SNyX53SSfTHKpJD+V5HfK9QALWH28AM11k/xk4TpsNtrYrxVy1i0AAugArFcncf21ykal1f18kpsVYGu9S1PGwm3+wTIW4HNCAVRmmGcBzBcm+bMkjx6ZL5ONd+3JSZ6d5FzFfKNVIrdbfgmI/nTh7zgNEOIcCMN2tuJU+HSSBxaw4y29U5EhoNIXOT6pePXIp+3LuzKf/07CWdG2cxdT3NjG+KWxOd24hBi8LMlvNZ2t+y63uvg7MG1VnHvbWeWXbICWFzlT8dDRaP43yf0WmHnMFtrUw5I8opml9QOkAJovruf8QZLzFG3ppYXTsuF4+zwHUL2maOt3KP3ZnG9O8tqy2Wxc7ayFz7lbkmeWn206lheU8QGr2oRPGI9QidZs/a4kLy9gXZ/rnpsXMw6AtnK8c5LHFm0J0NEOmc1t87PnFVAWrkFeQEYs1C8W0xBpfcfSF6/pWF/fUbQ/fQwBFZjQVMf4pVVzAlC0U41Wtc673PrC78C0dZHuZYdMGebRXcuXth3k+5P88xIP3DcneUXRbGziNsyASfILJS7KwqdB2ci0KKYZ13k1CWlMvuiepTFHmIx/mOQS5ecAAmjVJihUPJB7aCoHGQuTjBnZtqcVDaUFJiYSjRGQmG8bDsC8+pMBvwSEzZfJJc6JRsbcw/XUBoDwUjRXMqpmG/MZkJAp7UdgZO3Lv2mntNS2LzJ7fpIfTfIfg/n4SPi957Qa5pQ5cXa8s/S37rvc+qLvwLR1ke5dh5Vfwh9YzC2XMWWwOCNfbiaYzWWTWbgCDX29mXFMN9qNJk6KJnKDFc+jrdkwIpNpCXcpnsA2Uln/by8gBxQ2HQtPpLkzP2urbn+u/9s0P2eSMfFumeSpAwE9vmiYwKXyXu28mZ7uAQxCLmq7chIaG83v95YIve2L/GhTOLF3NPcAKXL44cF8aDlMVOAyjF86yJymvMsp62itazowrSWuWV4sHunfiunBBFm3IbdpG8wG5h5TCOkqWHMs3QFw0bD+v3BGU57HxLGxrj64+PJls9nMgGubY/n+koLDvOSxrE0oxc8k+aFBuskiIKv32Us0Gc08WkKdZgZYh30ukw0tl4YIVKqZuUy2NDehHvglWl3bNp3TJu9yyvteeU0HppUimv0Ft0vyqCS/muQJa84GWDCtmDUAjgdpVascCO1gyvMQwkwW3JVo6bb9dpL7FvMG2G1zLNI2mLY4KyCqIcSBOO2SedmarTV+iekKIIeNZ9G9NK02Tqz2aZPTpKbI8JxJ/jOJ+bc8UpUtMlz0edt8PPBeTDIAVduUOd2iEPzDOa37Lletjcm/78A0WVSzvbDyS2OcxKpJ2UyvKl9sOViL3OptP0jfGnbw76sekOTShYfifkd+14Z/YZrI9btcAYlNx8IcouHVRvsBchJwef3ME8+Ey8JpAcqhdsm0YqYhlnkRjQl/VrWZ+xRz1+8B3RWT/EMxVz2biYX/mdKqpih16F+aGyp3V+fjOjLDg9EqmdeVX/K+pKZUnm7ZnCq/NJzTuu9yytwmXXO8AJOFx36fZab1pDc5flHll2yeIccytdvHFD7DRhsLuPSl5k2qxCl3Oa5lyIEseh4TjXYlPoqpWJtNh5fh9ufK1jYZCxNqyK35PxDiEPAM2o4/TDGckyoLNJ/a7BOhDsw//BI54NxoohqgAxCA+JeTAFWaKg+ltYezEtckFGKsDWXIlKT9nD/J+5ob7l+cDYAEl2cMvIH1A8KRgU+TqA1YcVTVBF00J3IHgLTEdk4eu+67nLqmVl53vAATu9tCH8Z9rBTQzC+oCaW8URb/Jg3A0LrIr90kNgNPGdPkz0vHlZPwAQAoUxowoDXZjDQijXeL1sXT1Zoym4xljOviVrdpaTcCJ4EIbUiYAjNJzBPtpmqI1g2CHhjQIph/TDvcmMbU5Y3jYgcovHnkUjVAgASkmIdtms+YDPUHLAR/AtBqlilpQh7Ma++Ch9PHAn9VgYksOSPI0n2VgN9kTpu8yynve9I1xwMwIQV9yaiyvCNHvflC8qRY3BcoqrxNwmxhUvjduqkmvr60IK59vAsSl1bwtwPvE77IBhWoN/Rojcm9bmhcFG+hoMoaKW4TDt37+tjGWACfTczDJWyByciE0xDOXPQ2NXlJ7RDQSOMR9PibBUjd27rkmVL+rx+bWtxWbfYZjo+phJheJkP3uB6YAE6eQJHnzDWBnQInaU7AHCdXPY00Q/FQuCegSbuswLrJnNZ9l1vdV4uAydcVkdfW7Nnqg3fUmflZZBYFMrF18+5oCEfmMbge5o7NR3NaVOdHVLYk4Cngh1fCw1R+SdSz53CPL7t/G2OpfQDDseJ44q6YwgC9pmrY4DY90BqmyVhrtBpa14cWvPVvLDL0vGUyrLcDbh8XJUyEZGg4I0BlXMO0F7FPglX9bowPXHdO67zLrS70RcAkPYGK2KruW33wjjpjyiADRTxrvvTrxvHsaKjH5WN4xUR/0wzqxjsuBdEnfWoJjAGTn1Ghbz1zYPJ1YrYwK3AXFyl/5q4FHpU1bJ0hnmlGw/ilozLHPo8NJTAGTGxqMSM8EHPWmMRm8BYhIOVsSRhliuxTjeYNX9vsb8NPiR7nskeciyliGk4x/2Y/+T6B1RJogenMxZvA/VhLOMgU19jM1R3s/+7j2eDOZH/zEFhgCOa2IRl5JPyevY6sY4Mr+cAW9jNRtxI4t9kQmty9PBRsbQFvyFveDARib4crAUGKyPnakMVI23aNHe4I+9MPVQItMIns5Qbl6lT6gu3PlaohjmuwnEXkC8fc44HREHT+zxMA2GpDxnEbcyvziOF4BIlJ9AR23KHuo91Q67fVZF5zB1cSkqvWfIZZ4Qd5HjkAcH9v2mgIYk+6prCpBPt9R1ICY6acADF1aIbBXVUAwIsblRYiaray/zY9V+YwgdF9NYlQiD03a+sF4XLmIXHNlMjiVS9CsJivMdd2bWJQeOcEkA1D+Vf1t+j3CFupCeJKNm0AiZu3Avym/fT7ugSOlAQ2ASYuRMFfNBxxExVMuFG5XmU28+i1TSCY8Hgq/LCAFc0GmC06uWMdgQM4NYUQ3q07u57+4VgiHsej1MTV9NYlsC8SoHwcuG0CTB6KvMQtASX/FgJPk1JcizdPINoYMMnfqdG99feACXAx86YkOC6btEJeYj8AZ9tE3NKYBL0xK49S68B0lN7m/OdyqMAkulhOjkBMB/5JZhTsVcMMDgOYvr2Q3TibYZMlreaOnKWpiZTzXyJ9Bl0CM5XAVI1JRKvoU1oSjeQvC2ELnGriZT2T7LA0pnsVXqktnVpfi7QUZiZuTNBlP2V2pgu2D/v4kMBUYJK3w7PF1EIeAySmVxvnNAQmnFEto1o5pmNlyuGolIJgFo61mvdTc5TGUhDWfeMI9lofaN176/WSQsmmLcmxaV/9vi6BIyOBMWBCUEugFAJQj4eRfS3RkgdK2IAwgmEZjFopsWpM7qmZ4ccSmBDeTpwQIrAof0tiKN6JSTcsr7HpyxQmQBM7iFeO5jY1r2zTcfb7ugRmJ4ExYOIGV5xK/JGC8sht/IzaMzajUg82NyCqlf/8XJiBnDT8kkxr/671jaUc4J9EXyPI28aDJ1OaBlZPx5gqSAmNCrArs3HPJTcBL3V2aFU9+nuqdPfzOuvR2pRQu6z5eFrHbY2n/ZxRH9XXSWBRrpzkSpHSyp3K+FZjpkZ1CyqkCclFcxqE5rQMR78InsTK+7fTH0SOi/Zm5ikXiv/xR30kFQMFckpNADA4LAXBaD+rGtMMAArQpLEgvkWeqyLQak0izwGqNBvPUDoC+DldQsVBxH1v85IAYFKp0XoSFuJv5Xeds9Y2H6BfKaVZxLH1JOEZvedl9ZikiyivoARFe7pEnZ6KkIIwaSvMkRrPRDsRONgeezMjkfShzkQCUqhUZaQZqXM0tt4AmHg7p7v4CG4jgHcm4pn3MI+HQnHzfkN99IskoJolzVd8mgMnx5r4Opo+jvH7ulk3n8XUgWk+76qP9NQSYKap7ihJXFrTWHOstxKzzHd1smvuZ5flnkugA9Oev6A+vIUSEEuH06QJoRLGWj3SW+4nIOttJhLowDSTF9WHeSoJVH7p/0opm7GAWQ4ZzhQn+UowHzshh+NE9gIulTYlZQk/iotaFIQrvUk8HieLooOcPMMyu3WwvNfKA7mWI0jSd+deJyzmDkwThNQv2TsJLOOXpEvduISPKK8jcXssoFbSOU3qyeWwR2af++pxUTx+bdMvj7F4OEemAzAZEUBPyEpLrPNC477wW37HeaTePA1PjbDeVkigA1NfInOUQOWXhKIgwGsTwvKzJYREwO2iAzeFqIinU2kCeNVWTT8AJeSlbSpUKDQo1KU2wcRCERymUMMRJLM7euphJdymXmuvAamTuta0esl1YFoto37F/kkAv6TwIH5pLDeygoPz8BQIbE0tms9zSs6nooitaaU2luOV6sm07cwFFjML68EWfnf7JGLq1JanMQn6VJba8/TdHjHOtJRVATB76xpTXwNHTAJnKpqQrANBuou4INrQgwow1UBgoqhFC5VeHp59x8snx3PsmC/mm4Mk/S1HklYkMbxtJ5bfK0godkpGBO1MPJV0KGZcD/ScsCC7xjRBSP2SvZIAbcahksvilwyYSUezclil03NrU3kVwEiBag+mqEdpS12SgjVsDuegadHSNJqWDAhZEhUckdvIdD+XCkObk28qSft4O57+QIumA9OBxNdvPgQJ3KqkIy2LXzIs/I/Ec+YcINIEWjrIFZDwrrWmFjJciWP155+9YF72S62LzyzTB9ADfjx8tdqEPNKDFj08BNHuzyM7MO3Pu+gjmSYBWglzbFn8Eu1HAjq3/rVL4rne5UvStnjLeNPadoNi2lV+SZqLAohyQ4Ec7518ztqkbCHXHdeNl2K2qc7KW+e5Pf1l2vscvaoD0wGE12/duQQqvyTmiIdsEb8kRYUHTO0w5XfqKTTVXJNjh2OqzT44uVTNwDHpF08kAVxIgcoZwxN25IS+uvRTE9ydEiSUYVgSqD6Hmeesw35M1Yql04Fp53urP/AAElAQUByRooWtd6x2KTdO/BEgURlD1YHWXHOdoocnlBLLVasRCsDtr3Af04y5xrTjiQNwuCgaUwuEOCxaFfd/7QcoMR2BZltEkTal1jzzThWM3jow9TUwcwkoc+LkG2S1ul3OKgQUzKwKCPgdJheNCs8DRGgmY41LH3F+SiGllcTBEalZr5SOwx08xzFjIraV1GHKIbF54dwvbonWxos3jOSmWSkZ5PiwWjHVHOTzeWZvEyTQNaYJQuqXdAl0CexWAh2Ydivv/rQugS6BCRLowDRBSP2SLoEugd1KoAPTbuXdn9Yl0CUwQQIdmCYIqV/SJdAlsFsJdGDarbz707oEugQmSOBr3H9VdGNaHv8AAAAASUVORK5CYII=)
Tan A = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,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)
So the ratios are cos A = √7/4 and tan A = 3/√7
Question 3.Given 15 cot A = 8, find sin A and sec A
Answer:Consider a right-angled triangle, right-angled at B
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHsAAACkCAAAAACSxA5ZAAAABGdBTUEAALGOfPtRkwAAClhJREFUeNrt3FmU1nUZB/A5p8u67qqrOpULaaaItrggVliamYIEh1CPKSm4MBZhpgJDxmgLLqUWWm4BpVS2nDygeSgtCze2SQ1EmBlm3u2//LZn+3aBdLQFdAZ/70U9d793Zt7PPM/v+T3vf/4z7/QgS3DtSXwtiT2nkGoGgJ48tvgAKSoFqnaIoRMy2lyHRNRqey8xRiLLaIMaqWxUVRG1jhRcymhXo4nL2oYcfB2i8zltNyoltl61dt1NPxOoj8hZc3Xhz5+du+mZr/YFFlfn3G+jDm543yvAzqfaRTLLmTcHeukjM1E4wEexlPV8t4pnD7kA5Io6KvLacG5w6nQpKucjm1nW810XftHxL1sMrKoqmtHWusTTZ5z1881/HGgKoDltYS3qjbfcu27roDOIo5xnTEIdgcYIAEkhSNZea6EeLUsAUBZknWup7SikaK99LJcN37JW5/UP5bIlpuiSpC7YKqlWWC1dsC0Uqb7lDtJu5B1HsO7tM9CNXqPI6885ZHbWXjNIJ4C9cPGlM67Ja2tiX7SUgHtOer5vBnL2mgWP0FTCH469GUtmIuTcbw2RlXj32ac5LJ2FvOdbqpId+o7dRlg+LW+fh4ID27oTbofD8s/lnaluFMDA2ef7uoVF09HJaHNNFNJXjn8p+jaWfT5rr5GD0p0n/g7RGDdMzztbgseWaVfszXfJtLz7rWn3wpm7SlYYlma2gR8euxElumAb/jp5GaLrho1tUy/ukIl1wU7XfmAnQoR2wX7siJ+jrvdYtHx2KiBVwpaZ8ylFqULOvDUETlrNP2ILyoJrytpr5XAEfnn8nWa1E0LWXkvO8zMfvC4llwyQnPsNhGLP+VOakmo1YooZ845t9TdN3A4VDw5EWXstYePhK7AbpYMKp5z7zRiYfFHd9saaGjFlmalK0nRSmBVL3rMFhAho0jwz1UiTGw7A2sN/AV+6fT9/5bEFXCq2nzEbCE1CRhtS1QyMXvnpoXKPicSsdlvqEbn1qHVIZYGYMtoaBMk9edQ3tQNuJcu531xqgfaln6gqCiGUyGlrMq7umPg0ole1UGWxpQ1Ag1rCY8fdB4MAMMnR50beYpkquKGRC77A/t8+/hbaWkOLUgk6uOzErXj9Pby3uuYMqtUIeODQNfvuzeeyoS6BIjYf3cdCXOW0jaJ5Z6MXfrrTZKcxo20hmnqjW07eRjGFZtb9NjYNeHzSjSoUmylmtV2pNnz2rNpgJtCMthTCaNz04b/9t2/tLbS5wR17/PB70QXb4h7d8rm+oa7YRNXiKTssdcEG7K7jHjWvXbBFtxx2mzK57LYBIzMurJsaOKctxuBR4AeHNbkBzrvfGmMteOqI+zBiVFtOWys1TjtnXBKDWKCcZ8xqrxWGek9tesdNjXn3W3jYfnPYryNrVXIz6xmTQbOnTu3zDasbZpTV5kH2809sjAoNsSbNaWtH/AOH/qWmypQpjebpNYWaBWYMHLpCSA2AQfPYiUPkl1Manjqz2OkOeB4Opq3m1RkX6Vvv3hxjS3PaYsamVj9ywgMyYlLltM3xkLTKl0++ugInrnPaoFp5tJx15naf2mnIsto6wuTWvXeDo2ZHU9b9tpo72PHuFcFKEWjHMtr0imhz3ukl9v6KM2fNrUNo33PMhjf8+Qf1fJM+8b7VFXXDNmybM6fUYc1vW+QbTngBBXcjb6yfsJYgwbpgj0xaXraoU+e2VZGuOaVhWu/RnDUXJSkiVk/4DWq1wnLaFAZjxKajbvFwps2sZ0wRK+t89sJR42SxlKx2LMzffuhOeAFHzTrXbDthw0d/kiDQaBZz2uyxY8rSwpuRC3jDzXZw+lx47ul/T6TsalaOOWwFG8BAc/3EtcCgB2ChynLGorRJqOXw7KeuK00a8ibbZDy2OdHOSBou556+Oxzw0vDg2lKThuTxo/c+02ItkmW0C6ZgHdl45M2hpkidnDXvCFc0PHTq9OEqBt0jWWuemuRx5eSBlq8S7Qo5bexqGJ54z2qxdghtqTSDLWYKKLTFGJ28oFkKvDrK0uc1s1MrKSa4y855xTC2GJNNyk61U9swfjbhoeA1qy0JEIHbeHR/Q9Uy2kmNSMzgTpndRqSsNoM7TpVv/Mg2kBSS0Q5O4RX2u8PXOKljzJk31wIS2vWZ3pbzWnFOW9gs0kjfp/7OLIyUs8+DV2H89pBHhQAb6/Ee40wtvaXnTlk+ygYT1py2pprlvKm7YYAyS9a8BwPunrJh79erZZ2pKLD5kNUgg+iYd3usvYb2pLkvk5ixvIF7OgfVrnDdh15IlUFJAMsyU8WYE8D49ZFrzFTMxADNYieEum6HtOukXu/pzV8sjCvvWox2l7hq2kY4cd4y2nGk5jrh4ZNWaorWiTnzBpJn3XzkVW1pc+xI1pqXrFHOPONFVE5copw1T20q8cOj/ooQkQhOMtqW2G885lagndQLpXHmDQD45gFsFojCFFXROmFeExaISd785amaGe0c2LZpbzz//OaNz19y7v7tyOaTMcNhycee5rHma6KqOxd/qffSefPmzZs379LLF1z01ePPPVDNNSZmS/HJD9yDOoy11hIMW7946b2rV61atWrVqp+sfnD1utmzDmCbqcagaefHL2nZmGcopGJsvez+1z4x+mZiv+9VtCTQxMqzp+0gbo51ppiQ4Lkv3qUqrwYplpy5//fNWWBEAu6Y+CtEao91looDsP2qlWT6agij7xzwfmseGTXxlg+uqFokSGM81xqR6IWFD2AfrezQd9YB3jcXCclGzztvhwwVnMZ8Pc7m46YLvo99FScqsXTaAfKuAhR3TvwDAhKN9XIcGs3w4vyV/1yrevRNQ9yfrXV02HT0zeOeYwoMLLj/NTMVB5ypoigap83aM17aFBi48r43Oc8rLD3iuRS6YFviDRNux6jvhk1DJ57faoau1NzmThlAM3bF/vFxjwGkOAjx4oJVr1vfcM6/2OTNKOBPfwYAwtPvX1QPViO7G61xRbPTGWo+c8Vt/1zvaUXfOwNAa91tDz6y5kUkxz1VRzk5N/0SBUtqz3/bzO/O6V102ZXji8u/cu3chQsmnXr95XuXC3svWnj1hy5EqEe+9q6vr5lz8aZYcQ8Lu4QnPnnWs0iMXQ9eu2Ll1Ytv/NZN/eOKb/StWNZ/2+Jlty/v7+/v719+84prFvd94xH4At87+QU8dtKtAPWYSYzp4Ts+8R1IiIK3NCISfjzp+p/2XfwkiqEecgn6l4cGpn6hUB9jMA5Grkw6rjAIOEH8q+tQiAVf1qnELz98xY/OPWsrt1o9WjUkrvz2+ssm/BaAq7RsMCXRcdrsYEmw7+U7VtGR71hqy71TH8Xvj+3tCHpYKt310IaXNh3TC+dAmoJBAwmPJ9TIjCLtW4cylCk6i6Xd/5kNaE8+rYT1MCRc3Q9gzjsfdyVAClL2iccXAo4qMexdEQXluiatY+vL77j+4QUn3y1sPYD6HzyEJOsXPbH3Jqal8U8Wk71/L7rvmdgxKMLMmmuvu/vB5Wsr43z/x+Q/xP/t/y37H1IHQs2BQ+NgAAAAAElFTkSuQmCC)
Given: 15 cot A = 8
To find: sin A and sec A
![](data:image/png;base64,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)
Cot A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7aQ/7Zm27ZmZrb/25A6tpBmtpA6ZpDbOpDbOpC2tmY6tmYAAGa2kDoAOjqQZjoAOjpmOjo6ADqQADpmZgAAOgBmOgA6OgAAAABmAAA6AAAApk9YtwAAAAF0Uk5TAEDm2GYAAAClSURBVHjavZHJEsIgEESbgCQmQYMCLjEqzv//ozWQxfKope8AU1T3HB7Ax4jgARQDET269GLOPl29RBN50oemlwCchdj61GnrqMaW5Yjz0FeFdKxvFVATL6wA4znXYjV0eRDBQuyjQqBeikBRGc6eSvwQegd/ZdErNnei3axXAe5SwtgXvUnt3LJIxjKTXvaYmfRqlp7/c9RbDBbCtcCiVx+/8PwEqDwPQs7rsH4AAAAASUVORK5CYII=)
It is given that,
Cot A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAAAAAAAAA6AGaQAGa2OgAAOmZmOmaQOma2OpDbZgAAZjoAZrbbZrb/kDoAkDo6kNv/tmYAtmY625A625Bm27Zm2////9uQ/9u2//+2///bB41yzQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAhklEQVQoU61RXRODIAwLUzYQ5xT8wP7/H7oCJ467+aBn3kKapi3AFXgjxGvOTuo0fKMzX5s3MNQ/upp9eNsQ/Gr3r6YFdXv9IkuOSRZ5V0Y+8ogSd7Y+6EU2buo4+NED49Mknu/j/nOuV7Fl0hmLjJ7Mwz8ANFR8Wvr0SQ85QoMsx7Wn1/sCZFoFKwbzI34AAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Let AB be 8k. Therefore, BC will be 15k, where k is a positive integer.
Pythagoras Theorem: It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
= (8k)2 + (15k)2
= 64k2 + 225k2
= 289k2
AC = 17k
Now we know that,
![](data:image/png;base64,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)
Sin A = ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
And also,
![](data:image/png;base64,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)
Sec A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7aQ/7Zm27ZmZrb/25A6tpBmtpA6ZpDbOpDbOpC2tmY6tmYAAGa2kDoAOjqQZjoAOjpmOjo6ADqQADpmZgAAOgBmOgA6OgAAAABmAAA6AAAApk9YtwAAAAF0Uk5TAEDm2GYAAAChSURBVHjavdFJEsIgEAXQT0ASE9CggENExb7/HS3ADOUyVfoXDA3N4gGsDvMuT7sn0SFX9DVX7K2GNmklT93AgTaKqUelDfNmfMU6yLtAFdSn0BIRvRrIR1MKm9Ajn1fBgFkFeBo48xQF5JnoUuOHoe/g3ynOVUgs/dJZDxxdXDjDGrC9m51Ll1k452GbaEdnaFd4J+f0O+wYxeys093Vzm9KCQ6vfX687QAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAA///b//+22////9u2/9uQkNv//7Zm27ZmZrb/Zrbb25Bm25A6OpDbtmY6tmYAOma2OmaQkDqQOmZmkDo6AGa2kDoAAGaQZjoAZgAAOgAAAAAAy6Wd2gAAAAF0Uk5TAEDm2GYAAAB3SURBVHjavZDbCoAgEETHtOxm2UWz9v//MwxLfQyi86AcZ5YFgdewwfjTEhEZoFvc5TMHWytf6E1oSo3UQ/y4DHfwO2bjxpO493tUjD+GcvALwhFNPP6oVRC7erzYG2A0Sa658G/pvI7zhWvBbOyXR+6oj2zfC04d7Adj00FDrAAAAABJRU5ErkJggg==)
Question 4.Given sec
calculate all other trigonometric ratios
Answer:Consider a right-angle triangle ΔABC, right-angled at point B
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
If AC is 13k, AB will be 12k, where k is a positive integer.
Now according to Pythagoras theorem,
The square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in ΔABC, we obtain
(AC)2 = (AB)2 + (BC)2
(13 k)2 = (12 k)2 + (BC)2
169 k2 = 144 k2 + BC2
25 k2 = BC2
BC = 5 k
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=
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![](data:image/png;base64,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Cos θ = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAAAAAAAAA6ADo6AGaQAGa2OgAAOgA6OjoAOmZmOma2OpDbZgAAZgA6ZjoAZpDbZrbbZrb/kDo6kGY6kLbbkNv/tmYAtmY625A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bsvReGQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAi0lEQVQoU62Q6w6CMAxG2ymg4uYFwQ10Y3v/h6QdI0BiYkj4/jSnXbvkAGxOeGe881GIF6rmrJi9fEErap7oOKe4Ys26jO1p3vL6zDphaI5f6lpC+6DXSCnBX7kS7xy+usjO13+dS/7MCcVt9heef/311X3pq8HDigG6nP2M/ryswTEnf2Dy8b9tGQA2uAb0F/z3pAAAAABJRU5ErkJggg==)
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Tan θ = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AGaQAGa2OgAAOgA6OmZmOma2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkDo6kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bFVaz0gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAf0lEQVQoU6VR1xKAMAij7r1x8/+/KbV1VB96p7z0ckmABoAvhUIIp7mcWJhdXpj1kSlZfNNDZXwKqGrgzlPH4/Ivi9o9vNm97IbfCuo82WPMVCZ9mEm8pjUMKlPcea4lMDGqiA5+0JFqjBpS606smhnOnLG8lYhhTeT7uJP9LxsDvASIZiCQXwAAAABJRU5ErkJggg==)
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Cot θ = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AGaQAGa2OgAAOgA6OmZmOma2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkDo6kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bFVaz0gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAf0lEQVQoU62Qxw6AMAxDU/beZef/fxMHihgSBxC+VC9OUsVEr8WNIzN9olSAt/UT4TkuqbMqcfTqQ5N3ZR2u5d3vZPxgbZBre0B1BI4ZuhUU0hzJC/5ZsvWkn7c/rJObtqxMAre79J3Rb9LZRyb32sP5Fq6Ii4rOPjf4Lv102gJ/ywSIeeas1QAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Cosec θ = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,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)
Question 5.If ∠ A and ∠ B are acute angles such that Cos A = Cos B, then show that ∠A = ∠B
Answer: 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)
To Prove: ∠ A = ∠ B
Given: cos A = cos B
Let there be a right angled triangle ABC, right angled at C.
Now we know that the side opposite to the angle of which we are taking trigonometric ratio is perpendicular, side opposite to right angle is hypotenuse and the side left is base.
So, now let cos of A and B
We know that,
![](data:image/png;base64,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)
Since for angle A, BC is perpendicular and AC is the base.
Now,
![](data:image/png;base64,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)
Since for angle B, BC is base and AC is perpendicular.
Given: cos A = cos B
Therefore,
AC = BC
Now, the angles opposite to the equal sides are also equal.
Therefore, ∠A = ∠B
Hence, Proved.
Question 6.If
evaluate:
(i) ![](data:image/png;base64,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)
(ii) ![](data:image/png;base64,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)
Answer:Let us consider a right triangle ABC, right-angled at point B
![](data:image/png;base64,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)
Given:
![](data:image/png;base64,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)
As, a trigonometric Ratio shows the ratio between different sides, cot also shows the ratio of Base and Perpendicular. As we don't know the absolute value of Base and Perpendicular, let the base and perpendicular be multiplied by a common term, let it be k
Therefore,
Base = 7 k
Perpendicular = 8k
According to pythagoras theorem,
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
= (8k)2 + (7k)2
= 64k2 + 49k2
= 113k2
AC = √113 k
Now we have all the three sides of the triangle,
Base = 7 k
Perpendicular = 8 k
Hypotenuse = √113 k
Now applying other trigonometric angle formulas
![](data:image/png;base64,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)
Sin
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjpmOjqQOpC2OpDbZgAAZjoAZpDbZrb/kDoAkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm2////7Zm/7aQ/9uQ/9u2//+2///b+n3FtQAAAAF0Uk5TAEDm2GYAAACiSURBVHjavdDdEoIgEAXgs5H0jylSCWrkvv87NotUTpc1dS5gh9nDxQd8HLYawFgS0aJKL2Gr01X06JRMcd8VPQBnwGedOvWgfG4ZWXEaceORjuu6AQaSDxsgaNmrcSuraWBrwCflYano2ZLyQXZ3LX4Yeg/+nckZfFkRHebObtkimJlzos2d5CxiOdlZHKc8nKOgS57OY2nArsbLGfH4hfMd4XQLklVav48AAAAASUVORK5CYII=)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Cos θ = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7aQ/7Zm27ZmZrb/25A6tpBmtpA6ZpDbOpDbOpC2tmY6tmYAAGa2kDoAOjqQZjoAOjpmOjo6ADqQADpmZgAAOgBmOgA6OgAAAABmAAA6AAAApk9YtwAAAAF0Uk5TAEDm2GYAAACiSURBVHjavdDdEsEwEEDhs21EVYPQxE9Fxb7/O7rQIeOS4Vzt7MzuxQefVSVVvW0AWV1Vt4AbapbZQH+e4zzQe2QdoM2muPIg0U9/7MWwGBuq1E0bF6BKHXZsHguJHtllQ5U80nfgVFWPc8AepuFn6Xv8O4mB0hncKUDhjN0vh7pwRmLXZlM40wfsxRTOrarqrXk5z9LmIf90jjrUEjWb75zv/HIN7zbNHYwAAAAASUVORK5CYII=)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAjCAMAAADPLogvAAAAAXNSR0IArs4c6QAAAJxQTFRFAAAA///b//+22///2/+2tv///9u2/9uQ29u2ttv/kNv//7Zm27a227aQ27ZmkLbbZrb/Zrbb25Bm25A6tpBmkJCQZpDbZpC2OpDbtmZmtmY6kGaQtmYAZma2kGY6Oma2kDqQOmZmkDo6AGa2kDoAAGaQZjo6OjqQZjoAOjoAADqQADo6ZgA6ZgAAOgBmOgA6OgAAAABmAAA6AAAAQAxN6wAAAAF0Uk5TAEDm2GYAAAD/SURBVHja3ZNRU8MgEIQXMKJglYYaY02tNmo1Nhpz//+/ORBMq1MTXtQZ72Uf2Nk7OD7gx0tTJb4/ZXdERCWAIh8IYTcCbKWc34z1WwLgG8VrGrD6MMi1OHq4GBhPu8lgiUqBsTAUuX5LMBbGa8NrMzkeCZMvCeZthn9WFFV/OqKNG+oyiQnjiygutFs0m5fdD/CaPpFf/y4XqQLS20dv65StznDaqk9csCsfbMtwn6DyVQUuwGYZIBfYYzu8nn5wgZNZJaDNHltBz9MtF655eI6vTSeN2XJhq4OuJyvuRa98oyAbE7jw8J5n/SLyXtPGPcgOF7ZVMSuQa/G7H+gdK40jPKIwDrcAAAAASUVORK5CYII=)
= ![](data:image/png;base64,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)
(i) ![](data:image/png;base64,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)
Putting the obtained trigonometric ratios into the expression we get,
= (1 – sin2 θ)/(1 – cos2 θ)
![](data:image/png;base64,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)
= 49/64
(ii) Cot2 θ = (cot θ)2
![](data:image/png;base64,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)
Question 7.If 3 cot A = 4, check whether
or not
Answer:It is given that 3 cot A = 4
![](data:image/png;base64,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)
Consider a right triangle ABC, right-angled at point B
![](data:image/png;base64,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)
To Find :
Cos2A – Sin2A or not
![](data:image/png;base64,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)
Cot A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7aQ/7Zm27ZmZrb/25A6tpBmtpA6ZpDbOpDbOpC2tmY6tmYAAGa2kDoAOjqQZjoAOjpmOjo6ADqQADpmZgAAOgBmOgA6OgAAAABmAAA6AAAApk9YtwAAAAF0Uk5TAEDm2GYAAAClSURBVHjavZHJEsIgEESbgCQmQYMCLjEqzv//ozWQxfKope8AU1T3HB7Ax4jgARQDET269GLOPl29RBN50oemlwCchdj61GnrqMaW5Yjz0FeFdKxvFVATL6wA4znXYjV0eRDBQuyjQqBeikBRGc6eSvwQegd/ZdErNnei3axXAe5SwtgXvUnt3LJIxjKTXvaYmfRqlp7/c9RbDBbCtcCiVx+/8PwEqDwPQs7rsH4AAAAASUVORK5CYII=)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAA///b//+2tv///9u2/9uQ29uQkNv//7Zm27aQ27ZmkLbbZrb/Zrbb25Bm25A6ZpDbkGaQtmYAkGY6Oma2kDo6kDoAZjpmOjoAADqQADo6ZgA6OgA6OgAAAABmAAA6AAAAl5pICwAAAAF0Uk5TAEDm2GYAAABhSURBVHjalY9HDoAwDAQ3CZ0Ueg/k/69Edo4ICeYyB+9Ka+BJ6jVJjAvbmYlcDIIsZyUm08IFYuUg34HMnwpfCRH8xi7hamhdjerK4+CDnfSG1IXNxGjpNeSex4es594LN/vJBa+hVLChAAAAAElFTkSuQmCC)
This fraction shows that if the length of base will be 4 then the altitude will be 3. And base and altitude will both increase with this propotion only. Let AB be 4k then BC will be 3k
In ΔABC,
Pythagoras theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
By pythagoras theorem
(AC)2 = (AB)2 + (BC)2
= (4k)2 + (3k)2
= 16k2 + 9k2
= 25k2
AC = 5k
Now,
![](data:image/png;base64,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)
Cos A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjpmOjqQOpC2OpDbZgAAZjoAZpDbZrb/kDoAkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm2////7Zm/7aQ/9uQ/9u2//+2///b+n3FtQAAAAF0Uk5TAEDm2GYAAACiSURBVHjavdDdEoIgEAXgs5H0jylSCWrkvv87NotUTpc1dS5gh9nDxQd8HLYawFgS0aJKL2Gr01X06JRMcd8VPQBnwGedOvWgfG4ZWXEaceORjuu6AQaSDxsgaNmrcSuraWBrwCflYano2ZLyQXZ3LX4Yeg/+nckZfFkRHebObtkimJlzos2d5CxiOdlZHKc8nKOgS57OY2nArsbLGfH4hfMd4XQLklVav48AAAAASUVORK5CYII=)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAA///b//+22///tv///9uQ29u229uQkNv//7Zm27aQZrb/Zrbb25A6ZpDbZpC2OpDbtmY6kGaQtmYAOma2kDo6AGa2kDoAZjpmZjo6OjqQOjoAADqQZgA6ZgAAOgBmOgAAAABmAAA6AAAAvUqlPAAAAAF0Uk5TAEDm2GYAAACbSURBVHjatZHZDoJADEXvLCg4jIKAuA4w/f9/NKWMxDdj9L60N12SngKfqqC7kSwbHYemEqu6G3vVO/G+nDP9yHUgoGilkl3N5nKAPlvVl0cDT3Qy4EDEq5uqmKws5H4dnA5ux347ThbZYFHHPX4tehf+psSPD475ys8v2BK/5BM/7m9Xfq8HLPxktELip7p8rid+qiaKJb7l9wR/uQy+la8VfAAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAA///b//+2tv///9uQ29uQkNv//7ZmZrb/Zrbb25A6OpDbtmY6kGaQOma2kDo6kDoAZjpmOjoAADqQOgAAAABmAAA6AAAAhO0BMQAAAAF0Uk5TAEDm2GYAAABaSURBVHjalY/RCoAgDEXvskyt1Mrc//9pbAUREdR5OdxtbAx40hYnorSog8/iPpK4mQ1lPyGwsOqg9oGubAZf4QP8Rg5XCwR3ZnfV4+0BUB5AyWqmkbn61607JtgEFNB6wsAAAAAASUVORK5CYII=)
And also we know that,
![](data:image/png;base64,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)
Sin A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7aQ/7Zm27ZmZrb/25A6tpBmtpA6ZpDbOpDbOpC2tmY6tmYAAGa2kDoAOjqQZjoAOjpmOjo6ADqQADpmZgAAOgBmOgA6OgAAAABmAAA6AAAApk9YtwAAAAF0Uk5TAEDm2GYAAACiSURBVHjavdDdEsEwEEDhs21EVYPQxE9Fxb7/O7rQIeOS4Vzt7MzuxQefVSVVvW0AWV1Vt4AbapbZQH+e4zzQe2QdoM2muPIg0U9/7MWwGBuq1E0bF6BKHXZsHguJHtllQ5U80nfgVFWPc8AepuFn6Xv8O4mB0hncKUDhjN0vh7pwRmLXZlM40wfsxRTOrarqrXk5z9LmIf90jjrUEjWb75zv/HIN7zbNHYwAAAAASUVORK5CYII=)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAiCAMAAACk7TNkAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAA///b//+2/9u2/9uQkNv/27aQ27ZmkLbbZrb/Zrbb25Bm25A6ZpDbOpDbtmY6tmYAkGY6Oma2kDo6kDoAOjoAADo6ZgA6OgA6OgAAAAA6AAAAEzK8QwAAAAF0Uk5TAEDm2GYAAABeSURBVHgBlcFbEoIwEEXBE8koE4Ko+Mrc/e/TIn5Tpd3smh6KGdI6cgpjk98GMFwLwEXPQndszuFl5OYwNcXMz/TF36qkMKhOV52uSrrR5eZs0v1MWo3cnLRIUdjzAYXcBMXloNd4AAAAAElFTkSuQmCC)
And ,
![](data:image/png;base64,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)
Tan A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7aQ/7Zm27ZmZrb/25A6tpBmtpA6ZpDbOpDbOpC2tmY6tmYAAGa2kDoAOjqQZjoAOjpmOjo6ADqQADpmZgAAOgBmOgA6OgAAAABmAAA6AAAApk9YtwAAAAF0Uk5TAEDm2GYAAACkSURBVHjavdDbDoIwEEXRXUBAoEqV1gsiwvz/P5oCgvpIoudpetJp0gXrEjQi0peA2j1EDoCuQ/IuguqWoA1QGdTeQubbecuAcmZ6J75HbNuUoCmmRluGU9ymY+Evq2MXETQGVRWgRUQuiV8/T8PPIt/h31HOfoCDvlpm8EHxlNfhGzjKFQP6CxwqO1jP4GT+M326gG+achxmcCd1qJx00QK+Jk+aLQ9CBPzPJQAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADo6ADqQOgAAOgA6OjoAOma2ZgA6ZjpmZpDbZrbbZrb/kDoAkDo6kGY6kGaQkLbbkNv/tmYAtv//25A625Bm27Zm27aQ29uQ/7Zm/9uQ/9u2//+2///bBXbt7gAAAAF0Uk5TAEDm2GYAAABkSURBVChTjY5JDoAgFEOLA46IIzjL/U+p1I0xMbGbt2j/b4G3xlQEJeDqDlPQ090Scm+UxyAiEphlhSPvsV3EKHn3V+LW3/gzxzq/MCWt0p5r5jyPwjitWli+jxmkDywyNF99JziMBE3w/ZS6AAAAAElFTkSuQmCC)
Now putting the values so obtained we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 7/25
Cos2A – Sin2A = ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAiCAMAAADF9REmAAAAAXNSR0IArs4c6QAAAHtQTFRFAAAA///b//+22///tv///9u2/9uQ29vb29u2kNv//7Zm27ZmkLbbZrb/Zrbb25Bm25A6ZpDbOpDbOpC2tmY6tmYAOma2OmaQOmZmkDo6AGa2kDoAAGaQZjo6ZjoAOjo6ADqQADo6ZgA6ZgAAOgA6OgAAAABmAAA6AAAAk3jCygAAAAF0Uk5TAEDm2GYAAADoSURBVHja7ZRbE4IgEIUXLQpNI1MsKbvn/v9f2JC3sNiannroPDDAfGcOMLsA/LRYWtSTcJv7boyXWC2a+XxVFrV1STjAO8XAL1G7lEU/OhVcRwBZYnmYzrc74mz8LGCsC8vDL2oy1USWRFyVdo53FAByT12pZup3yza+OZvymSbvNO5iJCJiYnYQFRHD9CGGv1qhrfte1i0r4WL++kJTU5tNrVbiI8Y7ziA0rIyIvnlmTN9SnleMTJpcRbS2zYQt+vAXDTVgpOpbMXGl2EygAIII2Fq4cwaMdzKlGgFLEavY9Ye+Z35EN+CFGaHv+8PGAAAAAElFTkSuQmCC)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAhCAMAAAAxrgE+AAAAAXNSR0IArs4c6QAAAFFQTFRFAAAA///b//+22////9uQ29u2kNv//7Zm27ZmkLbbZrb/Zrbb25A6OpDbtmY6Oma2kDqQkDo6AGa2kDoAZjoAZgA6ZgAAOgA6OgAAAAA6AAAAxTAmvwAAAAF0Uk5TAEDm2GYAAABvSURBVHjatZHJDoAgEEOLCyqiuCv9/w81uAZPGrW3pp1k5g1wQ6Ilyeb0VQhRS6+TGH/kGjdv4g9FX/hdcUc6NpqklQj6DKmVgFZHJRp9r4utvzJNd7TR5DranH8pVvCJWpC5PBjcWQqiJG3+eNsZjyAGiwI6chUAAAAASUVORK5CYII=)
Therefore,
Cos2A – Sin2A
Hence, the expression is correct.
Question 8.In triangle ABC, right-angled at B, if
find the value of:
(i) Sin A Cos C + Cos A Sin C
(ii) Cos A Cos C – Sin A Sin C
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM2OQAAkpIAAgAAAAM2OQAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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For finding value of sin A cos C + cos A sin C , we need to find values of sin A, cos C, cos A, sin C
![](data:image/png;base64,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)
tan A =
= ![](data:image/png;base64,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)
If BC is k, then AB will be,
where k is a positive integer
In ΔABC,
AC2 = AB2 + BC2
= (
)2 + (k)2
= 3k2 + k2 = 4k2
AC = 2k
For finding the perpendicular and base for an angle of a right angled triangle, always take the side opposite to the angle as perpendicular and the other side as base
We know that,
![](data:image/png;base64,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)
Now, for angle A, Perpendicular will be side opposite to angle A that is BC and Hypotenuse will be AC
Sin A = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PLvsALysCbKWAqqcAAAAASUVORK5CYII=)
And also by cosine formula,
![](data:image/png;base64,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)
For angle A, base will be AB and hypotenuse will be AC
Cos A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAiCAMAAACOXcLLAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjpmOjqQOpC2OpDbZgAAZjoAZpDbZrb/kDoAkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm2////7Zm/7aQ/9uQ/9u2//+2///b+n3FtQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAArElEQVQoU62QbROCIBCE9zTtXUqiUtQI/v9/7A7JqW+OtR+Ym2N3GR5gsYIuOesVEWXn2GJ3soEtenS5TO7Q8QyYCuEmd0HXQ96mVCUWU8JteSPHY3MBBu6jjAfLAa9qPBW3yxA011w5rqnog6a8teLdN4u/MCMoL3xpRua/lpEzwn1NdPzkbFYNbISYOEe0UYmzEEtKnIXjqDdnJ9BFE2evmLNh38QZ7vQD5xfhdAuS7icGEwAAAABJRU5ErkJggg==)
=
= ![](data:image/png;base64,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)
![](data:image/png;base64,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)
For angle C, Perpendicular will be AB and hypotenuse will be AC
Sin C = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAlCAMAAAB8mplNAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6ADo6ADqQOgAAOgA6OjoAOjqQOma2OpDbZgAAZgA6ZjoAZma2ZpDbZrbbZrb/kDoAkDo6kGY6kGaQkJCQkLbbkNv/tmYAtmZmtpBmtv//25A625Bm27Zm27aQ27a229u22/+22////7Zm/9uQ/9u2//+2///bZibmjQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAqUlEQVQoU51QyRbCIAwMtXXFpa5ohboUhP//QQOID7iVufAmCTPJABSDkx+Cwu2eaulNpi23AGJGKnw8BANzuEBfMc/NaXCvmmKjwzHlJT7HHcCzqweQreVXMsECmH0LwfTR2A6v3/aHpgyUK2h6dm6iCbY8mIUl1NybFiPkkOdRLDji42tNyCKa1zSK838hxpmAL1PexxI2xoxL5D55D72yt0aFERvj6BcAIgjaaSWYXAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
For angle C, base will be equal to BC and hypotenuse equal to AC
Cos C = ![](data:image/png;base64,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)
=
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PLvsALysCbKWAqqcAAAAASUVORK5CYII=)
(i) sin A cos C + cos A sin C
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
(ii) cos A cos C - sin A sin C
= (
) (
) – (
) (
)
= ![](data:image/png;base64,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)
= 0
Question 9.In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of Sin P, Cos P and tan P.
Answer:Given that, PR + QR = 25
PQ = 5
Let PR be x
Therefore,
QR = 25 - x
![](data:image/png;base64,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)
Pythagoras Theorem: the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in ΔPQR, we obtain
PR2 = PQ2 + QR2
x2 = (5)2 + (25 - x)2
x2 = 25 + 625 + x2 - 50x [as, (a + b)2 = a2 + b2 + 2ab]
50x = 650
x = 13
Therefore,
PR = 13 cm
QR = (25 - 13) cm = 12 cm
and we know,
![](data:image/png;base64,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)
sin P = ![](data:image/png;base64,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)
cos P = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADcAAAAiCAMAAADMHrFcAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOmZmOma2OpDbZgAAZgA6ZjoAZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY6tpBmtrbbttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2/9vb//+2///bob1I3AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABOUlEQVRIS9VUXVfCMAxNx4crok50AymKnUix/f//z6Rdq3IkLY/LS3ZOcpubZLkAYzHbCCFmewD3KsVsy9PWmFsNOXr+6boaXDffg568s0Dd/oTVA4Cq4UgQs+AL/sLZpoWDbF2H8DwOed6HkkYi5WcgOAByzu3FyMB1SPUMbUNFeQvEcBwhlSCnLlPOrbfIz9fTca5mhdQzLN3O93RmBc3924Jtlkvc//X29Zad5vWPliEULjhY/B3PcCkePy69+zexrHp5VpZn+VMjzYz6knTmYh9uV1OsvxXVUzhA0hfvFXNI/d2KcG79Ah8Vfgz64j1/EtrXQzMLOlivL8kz44640wZvcNAX70lG8zglpoiL1NBnVTDyPMikL6QzOB7uAJ26wbB9JI1J+uJ1RgtGz0jjKd7LsIdR2DdIjxdRdD7pPAAAAABJRU5ErkJggg==)
tan P = ![](data:image/png;base64,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)
Question 10.State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1
(ii) Sec
for some value of angle A
(iii) Cos A is the abbreviation used for the cosecant of angle A
(iv) Cot A is the product of cot and A.
(v)
for some angle θ
Answer:(i) Consider a ΔABC, right-angled at B
![](data:image/png;base64,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)
Tan A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AGaQAGa2OgAAOgA6OmZmOma2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkDo6kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bFVaz0gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAf0lEQVQoU62Qxw6AMAxDU/beZef/fxMHihgSBxC+VC9OUsVEr8WNIzN9olSAt/UT4TkuqbMqcfTqQ5N3ZR2u5d3vZPxgbZBre0B1BI4ZuhUU0hzJC/5ZsvWkn7c/rJObtqxMAre79J3Rb9LZRyb32sP5Fq6Ii4rOPjf4Lv102gJ/ywSIeeas1QAAAABJRU5ErkJggg==)
But
> 1
Tan A > 1
So, Tan A < 1 is not always true
Hence, the given statement is false
(ii) Sec A = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AGaQAGa2OgAAOgA6OmZmOma2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkDo6kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bFVaz0gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAf0lEQVQoU62Qxw6AMAxDU/beZef/fxMHihgSBxC+VC9OUsVEr8WNIzN9olSAt/UT4TkuqbMqcfTqQ5N3ZR2u5d3vZPxgbZBre0B1BI4ZuhUU0hzJC/5ZsvWkn7c/rJObtqxMAre79J3Rb9LZRyb32sP5Fq6Ii4rOPjf4Lv102gJ/ywSIeeas1QAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let AC be 12k, AB will be 5k, where k is a positive integer
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(12k)2 = (5k)2 + BC2
144k2 = 25k2 + BC2
BC2 = 119k2
BC = 10.9k
It can be observed that for given two sides AC = 12k and AB = 5k,
BC should be such that,
AC - AB < BC < AC + AB
12k - 5k < BC < 12k + 5k
7k < BC < 17 k
However, BC = 10.9k. Clearly, such a triangle is possible and hence, such value of sec A is possible
Hence, the given statement is true
(iii) Abbreviation used for cosecant of angle A is cosec A. And Cos A is the abbreviation used for cosine of angle A
Hence, the given statement is false
(iv) Cot A is not the product of cot and A. It is the cotangent of ∠A
Hence, the given statement is false
(v) sin θ = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADo6ADqQOgAAOgA6OjoAOma2ZgA6ZjpmZpDbZrbbZrb/kDoAkDo6kGY6kGaQkLbbkNv/tmYAtv//25A625Bm27Zm27aQ29uQ/7Zm/9uQ/9u2//+2///bBXbt7gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAbElEQVQoU42PyRKDMAxDZWgDbQlhKwmUJf//ldQ6cAFm0OXNyLLHAo6aTalmrHLSW6ecXlG5fvrobAMvqieDnAM/k/Yn584trovczu/BkEtS6HcthqSjPWfkUlvFVx4kMP6LrO8OLBQM9y60AV1sBE3Mf000AAAAAElFTkSuQmCC)
In a right-angled triangle, hypotenuse is always greater than the remaining two sides. Therefore, such value of sin θ is not possible
Hence, the given statement is false
In Fig. 8.13, find tan P – cot R.
Answer:
Applying Pythagoras theorem for ΔPQR, we obtain
PR2 = PQ2 + QR2
(13)2 = (12)2 + QR2
169 cm2 = 144 cm2 + QR2
25 cm2 = QR2
QR = 5 cm
tan P =
=
cot R =
=
tan P - cot R =
= 0
tan P - cot R = 0
Question 2.
If sin calculate Cos A and tan A
Answer:
Let ΔABC be a right-angled triangle, right-angled at point B
Given that:
As we know trigonometrical ratios give ratio between sides of right angled triangle instead of their actual values. So from sin A we get the ratio of Perpendicular and Hypotenuse of the triangle. Now as we don't know the exact value let Perpendicular = 3 k and Hypotenuse = 4 k
According to Pythagoras theorem: (Hypotenuse)2 = (Base)2 + (Perpendicular)2Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(4k)2 = AB2 + (3k)2
16k2 - 9k2 = AB2
7k2 = AB2
Cos A =
= =
Tan A =
= =
Question 3.
Given 15 cot A = 8, find sin A and sec A
Answer:
Consider a right-angled triangle, right-angled at B
Given: 15 cot A = 8
To find: sin A and sec A
Cot A =
It is given that,
Cot A =
Let AB be 8k. Therefore, BC will be 15k, where k is a positive integer.
Pythagoras Theorem: It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
= (8k)2 + (15k)2
= 64k2 + 225k2
= 289k2
AC = 17k
Now we know that,Sin A =
=
Sec A =
=
Question 4.
Given sec calculate all other trigonometric ratios
Answer:
Consider a right-angle triangle ΔABC, right-angled at point B
sec =
=
If AC is 13k, AB will be 12k, where k is a positive integer.
Now according to Pythagoras theorem,The square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in ΔABC, we obtain
(AC)2 = (AB)2 + (BC)2
(13 k)2 = (12 k)2 + (BC)2
169 k2 = 144 k2 + BC2
25 k2 = BC2
BC = 5 k
Sin =
= =
Cos θ =
= =
Tan θ =
= =
Cot θ =
= =
Cosec θ =
= =
Question 5.
If ∠ A and ∠ B are acute angles such that Cos A = Cos B, then show that ∠A = ∠B
Answer:
To Prove: ∠ A = ∠ B
Given: cos A = cos B
Let there be a right angled triangle ABC, right angled at C.
Now we know that the side opposite to the angle of which we are taking trigonometric ratio is perpendicular, side opposite to right angle is hypotenuse and the side left is base.
So, now let cos of A and B
We know that,
Since for angle A, BC is perpendicular and AC is the base.
Now,
Since for angle B, BC is base and AC is perpendicular.
Given: cos A = cos B
Therefore,
AC = BC
Now, the angles opposite to the equal sides are also equal.
Therefore, ∠A = ∠B
Hence, Proved.
Question 6.
If evaluate:
(i)
(ii)
Answer:
Let us consider a right triangle ABC, right-angled at point B
As, a trigonometric Ratio shows the ratio between different sides, cot also shows the ratio of Base and Perpendicular. As we don't know the absolute value of Base and Perpendicular, let the base and perpendicular be multiplied by a common term, let it be k
Therefore,
Base = 7 k
Perpendicular = 8k
According to pythagoras theorem,
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
= (8k)2 + (7k)2
= 64k2 + 49k2
= 113k2
AC = √113 k
Now we have all the three sides of the triangle,Base = 7 k
Perpendicular = 8 k
Hypotenuse = √113 k
Now applying other trigonometric angle formulas
Sin =
=
=
Cos θ =
=
=
(i)
Putting the obtained trigonometric ratios into the expression we get,
= (1 – sin2 θ)/(1 – cos2 θ)
= 49/64
(ii) Cot2 θ = (cot θ)2
Question 7.
If 3 cot A = 4, check whether or not
Answer:
It is given that 3 cot A = 4
Consider a right triangle ABC, right-angled at point B
To Find : Cos2A – Sin2A or not
Cot A =
=
This fraction shows that if the length of base will be 4 then the altitude will be 3. And base and altitude will both increase with this propotion only. Let AB be 4k then BC will be 3k
In ΔABC,
Pythagoras theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
By pythagoras theorem
(AC)2 = (AB)2 + (BC)2
= (4k)2 + (3k)2
= 16k2 + 9k2
= 25k2
AC = 5k
Now,Cos A =
=
=
And also we know that,
Sin A =
=
=
Tan A =
=
=
= 7/25
Cos2A – Sin2A =
=
=
Therefore,
Cos2A – Sin2A
Hence, the expression is correct.
Question 8.
In triangle ABC, right-angled at B, if find the value of:
(i) Sin A Cos C + Cos A Sin C
(ii) Cos A Cos C – Sin A Sin C
Answer:
For finding value of sin A cos C + cos A sin C , we need to find values of sin A, cos C, cos A, sin C
tan A = =
If BC is k, then AB will be, where k is a positive integer
In ΔABC,
AC2 = AB2 + BC2
= ()2 + (k)2
= 3k2 + k2 = 4k2
AC = 2k
For finding the perpendicular and base for an angle of a right angled triangle, always take the side opposite to the angle as perpendicular and the other side as base
We know that,
Sin A =
= =
And also by cosine formula,
For angle A, base will be AB and hypotenuse will be AC
Cos A =
= =
For angle C, Perpendicular will be AB and hypotenuse will be AC
Sin C =
= =
For angle C, base will be equal to BC and hypotenuse equal to AC
Cos C =
= =
(i) sin A cos C + cos A sin C
=
=
=
(ii) cos A cos C - sin A sin C
= () (
) – (
) (
)
=
= 0
Question 9.
In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of Sin P, Cos P and tan P.
Answer:
Given that, PR + QR = 25
PQ = 5
Let PR be x
Therefore,
QR = 25 - x
Pythagoras Theorem: the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in ΔPQR, we obtain
PR2 = PQ2 + QR2
x2 = (5)2 + (25 - x)2
x2 = 25 + 625 + x2 - 50x [as, (a + b)2 = a2 + b2 + 2ab]
50x = 650
x = 13
Therefore,
PR = 13 cm
QR = (25 - 13) cm = 12 cm
and we know,sin P =
cos P =
tan P =
Question 10.
State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1
(ii) Secfor some value of angle A
(iii) Cos A is the abbreviation used for the cosecant of angle A
(iv) Cot A is the product of cot and A.
(v) for some angle θ
Answer:
(i) Consider a ΔABC, right-angled at B
Tan A =
But > 1
Tan A > 1
So, Tan A < 1 is not always true
Hence, the given statement is false
(ii) Sec A =
Let AC be 12k, AB will be 5k, where k is a positive integer
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(12k)2 = (5k)2 + BC2
144k2 = 25k2 + BC2
BC2 = 119k2
BC = 10.9k
It can be observed that for given two sides AC = 12k and AB = 5k,
BC should be such that,
AC - AB < BC < AC + AB
12k - 5k < BC < 12k + 5k
7k < BC < 17 k
However, BC = 10.9k. Clearly, such a triangle is possible and hence, such value of sec A is possible
Hence, the given statement is true
(iii) Abbreviation used for cosecant of angle A is cosec A. And Cos A is the abbreviation used for cosine of angle A
Hence, the given statement is false
(iv) Cot A is not the product of cot and A. It is the cotangent of ∠A
Hence, the given statement is false
(v) sin θ =
In a right-angled triangle, hypotenuse is always greater than the remaining two sides. Therefore, such value of sin θ is not possible
Hence, the given statement is false
Exercise 8.2
Question 1.Evaluate the following:
(i) ![](data:image/png;base64,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)
(ii) ![](data:image/png;base64,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)
(iii) ![](data:image/png;base64,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)
(iv) ![](data:image/png;base64,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)
(v) ![](data:image/png;base64,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)
Answer: 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Given is the table of Trigonometrical ratios for different values. Use the values from table for solving the questions.
(i) sin60° cos30° + sin30° cos 60°
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 1
(ii) 2 tan245° + cos230° - sin260°
= 2 (1)2 + (√3/2)2 - (√3/2)2
= 2 + 3/4 - 3/4
= 2
(iii)
![](data:image/png;base64,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)
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N/DpDdhPDJ4hSrGegcATrwKZbY8PSAsepcIEP9cPpDZX2fpFMgRahIkiFvIDnVDnQYSpz3aZLeUkCqXfIDLmBBfAdkVaGXY7nKQnMAOozFQUHyMQFUAN4pDQfI/qIZF9GZqJHZaC5Ah8HYbwnjJbf0iJlYObIBy8yHmFHxAn8050ZYe05Az81rXz8jBxzoGZnvS6fjgAM9Ha99pYwccKBnZL4vnY4DDvR0vPaVMnLAgZ6R+b50Og78D1zDs5rrhS7WAAAAAElFTkSuQmCC)
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![](data:image/png;base64,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)
As the denominator has an irrational number, we need to rationalize the fraction
![](data:image/png;base64,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)
(iv)![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALEAAAAkCAYAAADGgts1AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAVqSURBVHja7Vu/btQwGDc7fYCi843sPd8KYqiOUMHIUKKbQDdU1S0dbqgg7VYxMQITTMAzlJWBPgFI7RO0z9ASO+frd47tOLGdy9Gv0jc0Odnfn9/3J8nP5Pj4mKCgrLOgE1AQxCgoawPi/O9ea0rle7W538qcf0fsjO0jp4WyabLVJ/0/yTTbaqKASRHd/Swbbw6Hw0+5fEx2s8chnNC206vs5BLaznUCZGgsRFN4f0QPcmWub4VdjGezB/L+bDbZSHrk5+J+L/k5mc02UsYyniwnJ5P7IzZ6Ozk5ud9UB558lNC/dZPPz2Z6BfcrdCBXii/OnzD2IZSd6yCz2fgBI+Rc+oClR89DYcG5gqrZA6+r2cU3fUbpdxhMEWCu3FyRV4x8JezVV3lf/s8VH2fZZojgHu5tDziIt/cOB6qOpi5hs6tqr16v90tNGgFimvxQ7QhpZ5Mq59otbWu7+mieyJcQuFB8sWAIPLmEWTGdbj+CwZEVbjRib2GFYbvZC7shgzOuFG8TA0LPyhVrcJZOk53hMHnP12aj6Rubc2zG8XsJJae5XjcLHWlyyn9b7hL0igO9iV2yygzI4JTrbgRxXlmWWmV+3dVOt2S9jRkd7R9UVTlTrFVfLvuKXnI/Ve2pAyn3oQ70IbCwDDRlQQGE/vCTGpxFiwTZc5Sy52JkyEGqy1aRXXMQ6dp8k9ZflaGuaxaBYheFnW52lYKUVxmzXQAoyljlKzxmeZu+kFVO/M/SrKrKmWIN7RR+mccMgms3292y7anDVL9P/qhFwxSjuljQOeQcZo1uUdeNQTUUc6AMHqzKtoysap28yuQgfqdWORdnwKpQVJUi8+s6lAdaViEX5wsQaSqey1inq2QiyQzrmeO0AGIp1mo84CgmqjqlP0SncrRBp4MsGqIre2JBO04Ulee2lfIANQVxeV2oeLPsW04MRVj6xQXERTDUNWQldtdLHRXgDO4yVoWwU33WcANxcU0Xa7XC6/bns389EJtBGrwSqw9wi8XS5HVdEJsyWyhumYOqgus7TlTNYLVBvDQqCLmBT9+qH2TVr2OnTZpWYr6/NtYyxqAS19nTNE7AdUJjoTxO9J9+lpWleGDJN6gJYnUdLvMWci4VSxn5wmezpZlZqaTeIJbzImiZ8p03bJPLM3HzqqD+luv3tM8+8zFq0Y75Q1ZNOx1m4sVYIF5lgfnU5GdjrHVvlEAcD/dePhxPx49se6oidADrqLO2Lxb0G8In8/kDC/zYofv4oV5T14EA1rZLYFQoEJeerud7lNrocPiNEvabg7jKrrofhUp+CAhgU0eAr7JsftbFuvp9P728HQP0exqBbIi1Lxbw0ybK+n8JRCegIIhRULoEYtt7SRSUrkgViK9RULouOE6g4EzcOQOQQH/nbeycAask0K/C1nWxs2kCtXFIoBNB7QKBvi2JSQ6PJU0PF7R1SCBIpfQhTXeFQF/HlibEchDAaOTwWHbaDheYpM1DAk4/spGnQ5Cm9cFuj0BvslPq7Essh6CMSQ6PYmc22TQdLrB1mzYPCVQDykKeDkGa1lWBlRDoLeRyH2K56seY5PBodtbUo+1DAk4g1hLlA5GmofNXSaA30Qt9iOVV64Qkh8e0U1dRbXNwrEMCXuOEligfiDRt3q9dAr2JXO5DLDeNSDqQdtpOhYprTdRIhwS8QawnT6c7IUjTutcwqyDQN6lQVcRynU0xyeGx7HStxKs6JOA2ThjI0yFI0x0j0Gt19iGWLz+BxyWHR7VTOVzQ5NVcrEMCTj+ykadDkKa7QqA36exLLDfaGpgcHtNO3eECFxC3cUjgv/5Ui3I3BJ2AgiBGQUEQo6AgiFHuuvwDsaCL1WxQ5KkAAAAASUVORK5CYII=)
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)
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XdaE7s746UhuvwvyvHVqxqQYRqzx3SFA235VreBIEk5swHSwQpa0UpiY5LXrrFk49zInE2yibr+W4lCYGTtSFZ+1NPstXPl0TeZWSffI2Zwqu6KXy35/r3kRBQlEbiSJshgTUIRJj+de6+jL5zaF82Xc+vL+XMpOx/y8hnt5K9ckkxlDRCDyj5F+fvyXEqSW+VM8gSmGORwLkIKEp2CAlIYJ5ApvAyCk8qoERuZsQTUcoa5ar1pkWCWXe66JJjVTLVnIwO2aOUKT43d9v3/oCAomSnkIAEFgkk1+KflTXJvy4H+WXarWrJeyXTgjmZ9r3A14ArlszgWZ96MHBy1cq8bloEFKVp+dvWSqAqgawtZa3pfwA5UHKdfUUZLSXdVbYtJLovI64vAmdXNcLrpkdAUZqez22xBKoQ+K9lfSnneeWoCosEOiGgKHWC2YdIYJAEkng1WUEWjz8ZZGM0ehgEqohSomkyH1zl2lWtTjbg7FdYtp9mGKS0UgLTJJAsDCZPnabvt9LqKkKT6Jt3l8XOdY2MKCXzwFfXrcD7JCABCUhg/ASqiFJfKDyzL4ZohwQkIAEJ0Mo7WVGyZ0lAAhKQwDoEJi9K60DzHglIQAISGBCBIY2UBoRVUyUgAQlIYB0CVUTpOiWXVbJOr1t+Btx6zQ146z7T+yQgAQlIYGAEqojSeYArbBh9l1Dw77uTe2C9Q3OnSCBncOWfJkoraw5NGGYd/SVQRZT6a72WSUACTRNIlvBvA19voGJFqQGIU6tCUZqax22vBFYTSALV5KfLicbJEG6RQOcEFKXOkftACfSWwP8s0/QP6a2FGjZ6AorS6F1sAyVQicAlgFOB5LvLqbAWCWyFgKK0Few+VAK9I/AY4L7AzVdYloCnHN63F3A+ICJ2WeD15Qj13jVIg4ZJQFEapt+0WgJNE/jf5RC+ty6pOO+JxwMfBz4/9/e7Ae8Ejiz3Nm2T9U2QgKI0QadvucnXAo4qX+VnbNkWH38OgZyX9A7gasAvlkDJ6OgTwNuAw4DflmsuXETqysD1StSeTCWwEQFFaSN83lyRwAOAa5bpnv2ACwLJPn96xfu9rF0Cbwe+AzxlxWMypfdp4LvlFNnZx0Sm8fLfbwzsA3yyXTOtfQoEFKUpeHn7bbw+kBfZKWW655aK0vadUizIulD8Eh9lCm9Zifjcv2yA/+DcBRcHvgRcBkjml5yZZpHARgQUpY3wefMaBHI2V9Oi9MdApgV/BZwE/HoNu6Z6y9NLxF1GsHXLLYBPAS8v03o5N63Jol+bpDmQuhSlgThqRGY2KUo5FfnhQNY2vgD8OfBA4KXAa4GmX5IjcsP/35SMbh4JvK9m45IL8/3AN4BHN3w6rX6t6YwxXa4ojcmbw2hLk6J0MPCtkoVg1vp7AO8Cso61LJJsGJS6sfIuwMuA/wacVeGRmcaL6Cfjwz2Bo4EXzgU+VKii0iX6tRKmcV6kKI3Tr31uVVOilK/pfwCSq+0Fcy/Vi5RR05llz02Vl22febVp2/Fl+u05azzkYsDzgUzhJQPEl9eoY9kt+rUhkEOtRlEaqueGa3dTopQIvi+Wr/ZrAD+cQ3JC2eSZMOUpRvjdsfD4Xzt0k6uU9bdERf5gze6UD4DPlqjKrBN+c8165m/Trw1AHHIVitKQvTdM25sSpbQ+ovNHZQ/NjMZs70z20twE+M0wMa1tdQTpTcDPS/v/z4qaMrrMvqRkadikZPovG2vfAByySUVz9+rXhkAOsRpFaYhe65/NCQfOOsDTKqwvVBWlKwGHAplaWrahcxWFm5X9Mk8tm3T7R2szi3ZiPROkB5VoxEytHbDkcRco4dv524kVzLkVkOi8BI8shn0nSOJVJTQ87Hf7CNCvFYBP+RJFacreb6bteRE9EXhY2Yu0W61VRSn13LTUnQi7Ktkfzg8cV0QsgQ67vSB3s7Vvf9+J9bWBTFtGkLJWlJLouA+XkO35tty7bJS9YYUGZjotqYWy2Tmh309YuCeRd68sSVwzhTfL9rBT1fq1AvipXqIoTdXzzbQ70z/HAHdfWNPZqfY6opR6Ek2X+vOy3U1kkgInYeERpF8208Te1FKFdYTpX+cs3qMEgoTh/PpSzkyK3zLy2a0k8CAphjKlFq7HLtzwmhKW/yLg8N0qm/u7fq0Ba0qXKkpT8nazbc0UUKLf3liyNFStva4oJTt1QrtznEK+1FeVA4FbA08um2ir2rPudVm7yn6oPK/O9OI6z1uXdZ6VKby/K6mAcnBfRjwRpQSHrFpvWrQx604XLb6e/1syOSSjQyIdM8V3Wo3G9dWvNZrgpW0QUJTaoDqNOu8D5LiDnL+z2whmnkhdUcq9eZH+Y3nxJSXOYskLMf9kz8zvyh+Tj+0rNW2r47lLAx8BbttBhN+6rGfteQbwZ0CE+6/LQX6Zdqta8p7ISDUn074X+BpwxZIZPIL5YODkqpXNXddHv67RDG9pkoCi1CTN6dSVF1GSb/4N8Jaazc46R77eM9VU9cs6X9XJOJCX4eIU0d5lhJTF9rPnbHkc8LcV1zhqNuE/Lu9KlDZhPd+urC1lrel/FCFdZ19RRkv7l6Ssie7LiCth+fPc67Dso1/r2O+1LRBQlFqAOoEqs6CdF1wiwb5fob2PBfYsiTuzuJ51inxZf7280I4oIcw7VZUD6HLdjeamy7LOklDkxQiybOy8UEl/U8G8tS7pSpTqsl7VmP9a1peSASNHVfSl9M2vfeEyWTsUpcm6fqOGZ1E7xxnsu8FXcl0Drl4W8TNdloX3RNrl6z/rSMtKpqyeW/chNa7vSpSaZJ2p1kuVCMUaTW310r75tdXGWvnuBBSl3Rl5xbkJZMolI5NM/2QfUVdllnT1zUBe1NsuXYhSG6yThSGBCX0pffNrX7hM1g5FabKuX7vhlwC+WiLPsmjeVUlfzT6cU4Hss9l26UKUtsW6S7Z982uXbfdZSwgoSnaLugSyIz/rElkLyImli+WZdStccf2yehK5FzHImsi2j6XoQpS6Yt2QyypV03e/VmqEF7VHQFFqj+1Ya04Yb0ZKdwPe07Eo5UiKJBJN9F6VzAGb+ODyQAI0MoW2rCSQIvt3Isw5XHBZiXAm20GVYJBl93fFehNOde9dJkpd+rWuvV7fMQFFqWPgI3jcbi/KNpuYkdKVOxKlHBOefVgJyV5XlLJ/69UbZOHeJus2/bhYd5d+7bJdPmsNAorSGtAmfstuU0pt4kmKm0SPOX3XJuXu6+6TX7tvvU88FwFFyQ5Rl0COipgFOuyU9qduvbtdn76azZo5+2cqgQ7bYr2bL5r8e9/82mTbrGsNAorSGtAmfsssTPmkkoizKxwJZU72gGyWfXFXD93hOV0EOmyLdZd4++bXLtvus5YQUJTsFusQyD6hfUq+uVmuuXXqqXNPEohGCJPjLqedbrt0IUpp4zZYd8m2b37tsu0+S1GyDzREINFvHyz5675boc588SepaDIKXK6sC+Xo7JxamizTVUpC0J9esl33YfNnV6JUl3UVlsuuacJH6zy7b35dpw3e0yABR0oNwpxQVbMkoTmP5/W7tDsvu4hJxCfJWBMmnfufDzyqHBqXM3l2KrPEnZ8Bnt0Tzl2JUh3W66JpwkfrPLuPfl2nHd7TIAFFqUGYE6vqnuUsoUzj/XqHtidXXfYW5dyl+ZITTRO4kKSuyaOXqblVJRnFc3RFkpP+sCecuxKlNLcq63XRNOGjdZ7dR7+u0w7vaZCAotQgzIlVlS/47C95RzmEb1XzE5gQUXpaOahv/roco35UCVx4yooKZofBJQlr9vz0pSRnW0Z7GQW2fcptVdbrstnUR+s8t69+Xact3tMgAUWpQZgTrCpHR0SU8iWf1EPLSs5BujPwOuBhCxfctWSszj6VHI+9rOQo9PytynHoY3ZBFdbrtn9TH63zXP26DrUJ3KMoTcDJLTcx5xs9FXgocMaSZ+XvhwCvKOcnzV/yQCBZv48G8u+LJfdmBPXwFXW33LTeVb8b63UN3sRH6zxTv65DbSL3KEoTcXTLzdyrjGRyhlHVnHTpexllHQDkq/m4BRuTOeKRZYosp5xaziGwDut12e3mo3Xq1a/rUJvQPYrShJzds6Zes6wx5WymTM8lT5ylXwT0Ub/8MQlrFKVJuLl3jcxx6MeUr/79gdN6Z6EG6SP7wFYIKEpbwT75hx4G3A+4Yzm0b/JAeghAH/XQKVMwSVGagpf71ca7lMCHg4Gf9ss0rSkE9JFdYWsEFKWtoZ/kg7PRNgfjHQ7MpwrKcRQKVD+6hD7qhx8ma4WiNFnXd97wvYGDgCMXghqyMfTQkgevc6N84LkI6CM7xNYJKEpbd8EkDLhqCfvO0eBnLbQ4WaL3rZBDbxKgtthIfbRF+D76PwkoSvaGtgnsARwPXAZYdszFJYEDgRPaNsT6VxLQR3aO3hBQlHrjitEa8nfl2IpVDYxQ7blDmqLRgulRw/RRj5wxdVMUpan3ANsvAQlIoEcEFKUeOUNTJCABCUydgKI09R5g+yUgAQn0iICi1CNnaIoEJCCBqRNQlKbeA2y/BCQggR4RUJR65AxNkYAEJDB1AorS1HuA7ZeABCTQIwKKUo+coSkSkIAEpk5AUZp6D7D9EpCABHpEQFHqkTM0RQISkMDUCShKU+8Btl8CEpBAjwgoSj1yhqZIQAISmDoBRWnqPcD2S0ACEugRAUWpR87QFAlIQAJTJ6AoTb0H2H4JSEACPSKgKPXIGZoiAQlIYOoEFKWp9wDbLwEJSKBHBBSlHjlDUyQgAQlMnYCiNPUeYPslIAEJ9IiAotQjZ2iKBCQggakTUJSm3gNsvwQkIIEeEVCUeuQMTZGABCQwdQKK0tR7gO2XgAQk0CMCilKPnKEpEpCABKZOQFGaeg+w/RKQgAR6REBR6pEzNEUCEpDA1AkoSlPvAbZfAhKQQI8IKEo9coamSEACEpg6AUVp6j3A9ktAAhLoEQFFqUfO0BQJSEACUyegKE29B9h+CUhAAj0ioCj1yBmaIgEJSGDqBBSlqfcA2y8BCUigRwQUpR45Q1MkIAEJTJ2AojT1HmD7JSABCfSIgKLUI2doigQkIIGpE1CUpt4DbL8EJCCBHhFQlHrkDE2RgAQkMHUCitLUe4Dtl4AEJNAjAopSj5yhKRKQgASmTkBRmnoPsP0SkIAEekRAUeqRMzRFAhKQwNQJKEpT7wG2XwISkECPCChKPXKGpkhAAhKYOgFFaeo9wPZLQAIS6BEBRalHztAUCUhAAlMnoChNvQfYfglIQAI9IqAo9cgZmiIBCUhg6gQUpan3ANsvAQlIoEcEFKUeOUNTJLBAYA/gx1KRwJQIKErD8va1gKOA+wJnDMt0ra1J4EbAS4DbAb+tea+XS2CwBBSl/rvuAcA1gcsC+wEXBK4LnN5/07VwTQIXAT4EXAC4haK0JkVvGyQBRan/brt+GRWdArwTuKWi1H+nbWjhQ4AjgdMUpQ1JevvgCChKw3LZuxWlYTlsDWv3Bq4OPAa4uKK0BsE/vOWPgUx9/wo4Cfh1I7VaSSsEFKVWsLZWqaLUGtpeVHwh4HFl3TDTd4rSZm45L/Bw4MLAF4A/Bx4IvBR4LfD7zar37jYIKEptUG2vTkWpPbZ9qDnrhycC3wY+qiht7JKDgW8BH5ur6R7Au4CwfuvGT7CCxgkoSo0jbbVCRalVvFutfC8gEXfHFCsUpc3ckVHSPwD/ArwAOKtUlyCSjJrOBG4+9983e5p3N0ZAUWoMZScVKUqdYO78IYmyy7Tdy+dekorSZm5IlOoXgasC1wB+OFfdCUA+Aq5nFOtmkNu4W1Fqg2p7dSpK7bHdZs0Hla/3b8wZoSht7pGIzh8Bn5irKutLny9h9jcBfrP5Y6yhSQKKUpM0269LUWqfcddPSKRdwvwX1zemJErXAbL+87Qae7KuBBwKPAf4RQ2n3Qz4JPDUElBS41Yv7YKAotQF5eaeoSidw3Is6XfOBzyxTNsthilPRZQiEmHwsDWylNy03JsIuyNYu4cAACAASURBVCoZTs4PHFdELIEOjpKaezc1VtPQRenxQDaXHl/2H2Qfwp8Ctyl7EZ7dGKl+VKQonRMMMJb0Oxkh5Uv/O0u61/5AXqLp22cDLwK+3o9u2JgVVyuBHXdfWPOZf8BuqbUSTZf7H1RBZA4rYeERpF821gorapTA0EXp6eVHvQjlTWXz4dg6Xh9EKXPy2efx5JrTJk103Kmk38kI6tMF2FjTDCW4I9FxbyyZSub7R53UWucpU5+fKyPOVf3sQODWpd/m49XSUwJjEKU/KdM5eWH9G/B24LM95b2pWX0QpUsDHwFuu4XIpamk35mCKN2nfDhmVmNxGq1uaq3kgvxH4FZA0nEtlvz3/PNC4HfljzcGvlJhdLXpb9b7axIYgygdDXy3ZrurXP5nwE+A71e4OF9r+XFl4+Os01e4rfYl7y9pZ65d8qLVrqCBG7YlSm2k3+mjj+OiWQaC7K0ZY4RYRkkJNvgb4C279MkqH2L5/b0P+Bpw+EJ96TcZIb2qTIPO/pwQ/L+tEVjRwE/HKqoQUJRWU8r8c1KS3HEXYcoPIskz71yEqU4kUBUfPRbYE7gMcEMgmwJPLusLWWs4Avh5lYoaumYbotRW+p2++HjmmisXf16yrJXmvyd8OX3qWStGAQ25tdNqspaWtbJE3e320VdFlGJ8jnPJbyFrjrPfYNas3lA+FucbeDEgferRnbbah1UiMCZRijhk2qOpiJqZ2Nx1B2Gqck0lRwzoom2IUlvpd6r4r8o1A3JfL0xN0EayKey7MHpZZlxVUUpo/b+WaeXsS0qQyIfLKGlZvc8AntsLGhpxLgJjEKV0wBuUKY+sK6VzZkrvnxvw9U4vpKm+rLoWpbbT7+jjBn4oNaoI70xzf7nsM9rt1qqiNJvyfHOJVNytXv/eUwJjEKWs4bx4bi3n8sCnypRaxGnTsuylNVVBCssuRamr9Dv6eNNfSfX7LwF8tURw/nWF26qKUt5lSR90KnDvCvV6SU8JDF2UrgD8aElSxecDh5T55WXROHXdMXtp/VWZystmvZ2m9erWn+ufuc5NO9zTdH2zR3UpSl2m39HHDXfAFdUlE0Myd2cNKJGyu5WqopR6cm3653/3WIrdsPb370MXpVVkDyh7H56wy96FOp6ZvbSS2uR7wO3LV1mdOna6tmkRWbe+jDQTXJH2LitZIL5XeaGs2u+Rc2peWWEReyce20i/MxUfJ0npI4B1f/8JvsgpyOuUhG9npHQ34D0VKqgjSjmS4ioejFiBao8vWbdT9qFJsT3TO8tOkdwP+ED54dyzIWPzwsriaCK2ct5N06LUkJkbV3PZsn8kbNcVpQSbvBr4wZrWbCv9zlR8nCi/R20gSjn64R1r+rZNUYqApW1j3XC8JvJh3TZkUXoe8KSSYiT7d+bL7YCc3HkskDQkm5bZyyoCl9Dv/KAjfGMVpp14dTF9t430O/p4019JtfvbnL7L7/1STt9Vc0RfrxqyKEWI7lQWNRfnpjO99PflcK9kHt6kzL+s7lA26mavUNatpihMXYjSKn+1lelAH2/yC6l3b46SmAU65Pyo3UrV6bu8y3LCbEbnBjrsRrXHfx+yKGXj28dLaOki4uyDeAyQDMRJJbJuWfaymtU1VWEamyjp43V/HevdNwsJPwlIwNBupaooZTtIDvXLZtlE41oGSmDIopS1j6S7z4hlPrVPFupzBHLOp8kaUBbd1ylhk4SvydGVjM3LUhlFmCKAyQPX9VTeto5v2KYoNZ1+p+8+XqffDuGe/Gb2KfnodkvLVTW1Vk6XjdAlx91Yc18Owbcb2zhkUUrjk1LkfuWMlG+W441zFECiel6wYR66RNnln0zZLTtaYH7ENPuR/UVHKfG3eXzDNkSprfQ7ffFxRg+Zcs5G4UxRZi9PPrpeX7ISbPxD71kFCUT4IJAcjss+9tZJrZUQ83xEJtHqmT1rr+bUIDB0UUpTM2xPfrpE9SQqLl9WSaS6aUmeudMqhjVnxJTgihzMliSabZZtH9+wDVFqi2cffJzfYM4Fy1R0Qq1nJSHTCbtOXsWxpcOZJWR9bRHeTf07S8j6GWBsZ6htymZw949BlAYHfUODt318w5hEaUNXNHJ7RkdJlfW2st3gt6XWTFVGpDJKvF754GrkgT2pJJGsOZMr03jLtnXUMTMjrhxdkajNH9a50Wv7R0BR6p9PdrKojeMb6hLIyzLreJkqGdshinVZNHF9EpPmQL9MY8W/s2O9Z5GGmY7KiztHPYypZLSUIIbsd8r677pldshfhD174ywDJ6AoDceBbR3fMBwC47Q04nP/Mk2cdZZZuTjwpXJkSY54SBaRsZUcLRFRyqgpqYfWKTkKPXsRqxyHvk793tMxAUWpY+AbPK6t4xs2MMlbWySQYIAkFs5enmQRWTeKtEUTG6k6QTtPBR46N0qsWnHufUoJLZ+NMKve63U9JaAo9dQxC2a1fXzDMChMx8oc8peAnW+Ug+jGHk2W/p2RTrZwzNbUdvN2MkM8skwld3nI5W52+fcNCShKGwLs4Paujm/ooCk+YgcCmcbLScdJlprprBy78sIaL2nhSmAUBBSl/ruxy+Mb+k9jGhbmuO4Ek2QKL9GWORDPIoFJEFCU+u3mbRzf0G8i07Eu+9GSmSCbaBPqnM3hFgmMnoCi1F8Xb+v4hv4SmZ5lLysba5PPLYdWWiQwegKKUn9dvI3jG/pLY7yWJVdbss0nu8Fi2HcW8l9VQsOTXDjnVFkkMGoCitLw3NvW8Q3DIzF8iy9YsjYkRVZCv3NS8nxJJvyc4Pu5MoVXNTJt+GRswWQJKErDc72iNDyfrbI4OROTiSBphLIPLYfUzZfXlD04Sfh7+HiabUsksJqAojS83tH08Q3DIzAui5Md/KLAGxeadZkybZc9SpniS3JgiwRGT0BRGo6L2zq+YTgExmlpfoPZOHoD4L3A14Arlszg2aP2YODkcTbdVkngDwkoSvYKCfSDQEZLOUwySVmToSBHe+ck1bP7YZ5WSKAbAlVEKfPe+XKrcu0qq5O3K5FFu50y2U2rfYoEJCABCfSSQBWhSWRQUsxHnNYtEaVk8/3quhV4nwQkIAEJjJ9AFVHqC4Vn9sUQ7ZCABEZLwPfMll2rKG3ZAT5eAhLoFQFFacvuGJIobRmVj5eABCQggbYJKEptE7Z+CUhAAhKoTKCKKOUo5uw6z8Fj65afAbc2Bf+6+LxPAhKQwDQIVBGl8wBX2DD6LqHg33fPxTQ6la2UgAQksC6BKqK0bt3eJwEJSEACEqhFQFGqhcuLKxK4FnAUcF/gjIr3jOmyzC4kp91eQBLoXqIc1vd64MNjaqhtkUDTBBSlpolOt75kub5mefnmfKAcy5CN16dPDEl+U48HPl6OpZg1/27AO4EjS167iWGxuRKoRkBRqsbJq3YncP0yKjqlvHxzSOEURSmjowQGvQ04DJidgZTs7p8Hklg3R1V8e3ekXiGB6RFQlKbn8y5anLRUUxWlmwOfBr5bkqvOpi9n52DdGNgH+GQXjvAZEhgaAUVpaB4bhr1TFqWIz/1LtOkH59x18XI+Us5JyjaLxaPPh+FZrZRAywQUpZYBT7T6KYvSKpffAvhUOfY803pJUmyRgAQWCChKdok2CChK56aajefvB74BPBrIabIWCUhgCQFFyW7RBgFF6ZxQ8AcCVwXuCRwNvHAu8KEN7tYpgcETUJQG78JeNkBROrdbLgY8H8gU3kNMt9XLPqtRPSGgKPXEESMzQ1H6Q4deBPhs2ceVyMRvjsznNkcCjRBQlBrBaCULBBSl5V3iZWVj7RuAQ+w1EpDAHxJQlOwVbRCYsijdCkhGi9cuCft+JPCqEhp+M+A3bcC3TgkMmYCiNGTv9df2PohSMii8FHgy8IuOUCW1UrI2JJPFy4EnLDw3kXevBD5XNhfPsj10ZJ6PkUD/CShK/ffREC3sgyhdGvgIcNsO8++dt6QYShqh5AI8dsF5rwEeDrwIOHyIjtVmCbRNQFFqm/A068+enESaXRs4bUsItiFKaWqyg18UeONCu5PJ4Utlj1Km+LbFZUvu8LESqEZAUarGyat2J/BYYE8gL98blkMhTwa+Xg53PAL4+e7VNHbFtkQpv6kHATcA3gt8DbhiyQx+AeDBQLhYJCCBJQQUJbvFWAlsS5RmPDNa2r8kZY0Yfwz4oqcvj7W72a6mCChKTZG0nr4R2LYo9Y2H9khgEAQUpUG4SSPXIKAorQHNWySwbQKK0rY9MLznP7Nhk5uub2ZeF6LUtO1N19ewq6xOAu0TUJTaZzy2JzT94ly3vssDCa44zwrAFyqRcG8HfrXimhwfkX1D31/TSevavupxTde3ZrO8TQLbI6AobY+9T96MwGWBxwCJaFtWqohSMiq8GvjBZqZ4twQk0BQBRakpktbTNwJdTN/1rc3aI4HBE1CUBu9CG7CCgKJk15DAAAkoSgN0miZXIqAoVcLkRRLoFwFFqV/+GKM1ewA/3kLD+ihK22KxBfw+UgLrEVCU1uPmXdUI3Ah4CXC7LRwD3jdR2iaLat7yKgn0gICi1AMnjNSEnLT6oRIdl+SsXR/T0CdR2jaLkXYxmzVGAorSGL3ajzY9BDiyZMOeuihtm0U/eoRWSKACAUWpAiQvqU1gb+DqZR/RxcsxFl2PlHLI3/OBpwO/rN2C5m7oA4vmWmNNEmiZgKLUMuAJVp9Nq48DjirTd9sSpT6gl0UfvKANgyKgKA3KXYMwNieungh8G/goMGVRksUguqxG9omAotQnbwzflr2ARJkdU5oyZVGSxfD7sy3YAgFFaQvQR/rI5KDLtN3LgbMmLkqyGGknt1ntE1CU2mc8lSccBHwB+MZcg6c6UpLFVHq97WycgKLUONJJVphIu1sCb11o/RRFSRaT/AnY6KYIKEpNkZxuPecDnlim7X49cVGSxXR/B7a8IQKKUkMgJ1xNRkjPAb6zhMH+wPmB44GzgRcBXx8xK1mM2Lk2rRsCilI3nKf4lIwaPl0avo2MDn1iLos+eUNbek1AUeq1ewZtnC/i/3SfLAbdlTW+SwKKUpe0p/WspPlJNF7Cw28C5OjxqRZZTNXztrs2AUWpNjJv2IXAlYEjgEsC1y/Xfh74BfAs4JQJEZTFhJxtU5shoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohoCg1w9FaJCABCUigAQKKUgMQrUICEpCABJohMAZRejxwfeB44CTgV8CfArcBfg08uxlUvanlWsBRwH2BM3aw6nLAY4ALAmcCZwMfBD7Vm5ZoiAQkIIEFAmMQpacDz1ni2TeVl/IvR+D1BwDXBC4L7FeE5rrA6SvadivgxcDDgS+Xa64GvBx4BPDDETCxCRKQwAgJjEWU/gTYA7gI8G/A24HPjshfGQlmVHQK8E7glsAqUbo28AHgnsCn5xj8E3D7MoI8cURsbIoEJDAiAmMRpaOB747ILzs15d07iNL5gPcDvwfuVKbsZnXdDbgz8GTgpxNhZTMlIIGBEVCUBuYwYCdRuhnwSeBhwBuH1zQtloAEpk5gbKJ0HiCjhd+M2LE7idKLykgo4pTpy0sDFwNOLUEfI8Zi0yQggTEQGIsofQK4AXDhsq50dSBTev88BicttGGVKMWXHwX2BRKhl+jDnwM/AQ4o05svHLlgj9DdNkkC0yIwFlH6XYk2y/+mXL6EPh9ZxGlMXl0lSgn9/nwJgMi6UaIPZ9F55wXeVUZMjwZmnMbExbZIQAIjIDAGUboC8CPgrAV/PB84BLhRiVobgbv+owmrRCmjxK8A1wAeB7xiocEJfEgQxP5lv9JYeNgOCUhgRATGIEqr3JEpq4RPP6HszxmL23YaKX0BuA5wC+AzCw1OCPlXy4jpwLHAsB0SkMC4CAxdlGL/BVYs4meTafbrRJiyZ2csZZUoJcjj4yVcfO8iQPNtvlIZMUa4IlqLI8ux8LEdEpDAgAkMXZSeBzwJuHuZmpp3xe2ADwHHAvcYsI8WTd8p+u4Y4CBgJ1FKhoebjjTgoWoKphF1B5sigXERGLooZY0kayX3Llkc5r1zL+DvgRcAT+vQbVnbeWkJzf5FC8/dSZQeVPYnJePDfDaHmDGbvsvo8Q5lg20L5nVeZd0UTJ0b6AMlIIHqBIYuSokky5TVLL/bfMuzZycJSbNnJwEAXZXsDfoIcNsdctNtYstOopSgj6wbZfS4uHk2oeInAAcDb9nEgJ7dWycFU89M1xwJSGCRwNBFKQlKk70gkXbzYc4JCf8X4K3AMzoeFbQtShkdZk0oOe5OW9KljwD+Esj0ZbKkp8TPEak9y9/+faQ/hZ0Ee6RNtlkSGBeBoYtSvJGQ7/sBxwHfBK5Xsoa/p0zddb0npw1RemwRlMsANwSy7+hk4Oslv12EKBtlUxL4kQzhseO5QATo0JJl/KElfH5cvfg/W6MojdWztmsyBMYgSnFWsoPfsaybfLsEPSSTwTZKG6K0Tjuy6B8mEbBMJ36x4xHjOjZveo+itClB75fAlglUEaW81K5YpoDWNTdZq783kUwCfRGldX015PsUpSF7T9slUFFoErWVH3vEad0SUUrYdhbhx14Upe15WFHaHnufLIFGCFQZKTXyoAYqeWYDdcxX0XR9s7o3FaW27NoN37aeu5tddf6uKNWh5bUS6CEBRam+UxLZl8CDZFBYVi4EZI9UTr/91YprMnJ8JfD9JX/fljis+9yrliPW1+1LSSKbrBtNFEWpCYrWIYEtElj3RbJFk7f+6IShZ/9TotzWFaWc9/Rq4Adbb83mBlwZeFTFqeBlT0vao3dsbsZ/1KAoNQTSaiSwLQKKUvPkN52+a96i6dSoKE3H17Z0pASqiFKyTucQvUtuwOBnwK1XZF7YoNpe3qoobc8titL22PtkCTRCoIooZe0k6Ws2ib7LBtasn5zdiNX9rkRR2p5/FKXtsffJEmiEQBVRauRBW6hkD+DHW3iuorQF6OWRu6Vg2p5lPlkCEqhEYKyilNRDLyn5335biURzF3UpShnFJtJvL+B8wCWABGK8Hvhwc03qdU11UjD1uiEaJwEJnJOoc2wlKYdyjlKi45K4dKyiFN89vmRJT1j1rNythFgfWXLfjc2/tkcCEhgxgTGK0kOAvJCTQXvMopTRUQJQ3gYcNie+Oc8pIpVQ7SSnTS5AiwQkIIFBEBibKOXE1auXfUQX35IoRRRylMbTgV+22AtuXg7y+245afaM8qxM4+WAvxsD+wCfbNEGq5aABCTQKIExiVIyKTwOOKpM321LlBp10A6VRXzuX6IaPzh3Xdr9JSDHXCScP4lwLRKQgAQGQWBMopRjsU8s01UfBcYuSqs6WKYsPwW8vEzrJaWRRQISkMAgCIxFlLK+koi7Ywr1qYpSNjgnLPobQI6KP3MQvVAjJSABCRQCYxClRNll2i4jg7MmKEqZxnsgkMSo9wSOBl64hahDf1QSkIAENiYwBlE6CEhSz4wOZmWqI6WLlSCLTOElCvHLG/cQK5CABCTQIYGhi1Ii7W4JvHWB2VRFKRiyT+uzZRNt2Hyzw/7koyQgAQlsRGDIopRpqyeWabtfK0rnIvCysrH2DcAhG/UQb5aABCTQIYEhi1JGAc8BvrOE1/7A+YHjSxLYFwFf75BrF4+6FbAf8NolYd+PBF5VQsNvBuT8JosEJCCB3hMYsiitgjvbPJq/byOjQxdOv2DJ2nDdMlJ8wsJDE3mXk20/V6Y3u0611AUDnyEBCYyQgKI0TKfmGJGkGEoaoezPOnahGa8BHg5khHj4MJuo1RKQwBQJjFGUkuYn0XgJD7/JiKeukh38osAbFzpuMjkko0P2KGWKLzkALRKQgAQGQWBMopQEpEeUE3KvX+gnMekvgGcBpwzCI9WNjO8eBNwAeC/wNeCKJTN49m49GDi5enVeKQEJSGD7BMYkStunuR0LMlpKYEeS0f4c+BjwxYmc8rsd4j5VAhJojYCi1BpaK5aABCQggboEFKW6xLxeAhKQgARaI6AotYbWiiUgAQlIoC4BRakuMa+XgAQkIIHWCChKraG1YglIQAISqEtAUapLzOslIAEJSKA1AopSa2itWAISkIAE6hJQlOoS83oJSEACEmiNgKLUGlorloAEJCCBugQUpbrEvF4CEpCABFojoCi1htaKJSABCUigLgFFqS4xr5eABCQggdYIKEqtobViCUhAAhKoS0BRqkvM6yUgAQlIoDUCilJraK1YAhKQgATqElCU6hLzeglIQAISaI2AotQaWiuWgAQkIIG6BBSlusS8XgISkIAEWiOgKLWG1oolIAEJSKAuAUWpLjGvl4AEJCCB1ggoSq2htWIJSEACEqhLQFGqS8zrJSABCUigNQKKUmtorVgCEpCABOoSUJTqEvN6CUhAAhJojYCi1BpaK5aABCQggboEFKW6xLxeAhKQgARaI6AotYbWiiUgAQlIoC4BRakuMa+XgAQkIIHWCChKraG1YglIQAISqEtAUapLzOslIAEJSKA1AopSa2itWAISkIAE6hJQlOoS83oJSEACEmiNgKLUGlorloAEJCCBugQUpbrEvF4CEpCABFojoCi1htaKJSABCUigLgFFqS4xr5eABCQggdYIKEqtobViCUhAAhKoS0BRqkvM6yUgAQlIoDUCilJraK1YAhKQgATqElCU6hLzeglIQAISaI2AotQaWiuWgAQkIIG6BBSlusS8XgISkIAEWiOgKLWG1oolIAEJSKAuAUWpLjGvl4AEJCCB1ggoSq2htWIJSEACEqhLQFGqS8zrJSABCUigNQKKUmtorVgCEpCABOoSUJTqEvN6CUhAAhJojYCi1BpaK5bA2gT2AH689t3eKIEBExi6KD0euD5wPHAS8CvgT4HbAL8Gnj1A35wHuBewF3A+4BLAZYHXAx8eYHuqmHwt4CjgvsAZO9xwOeAxwAWBM4GzgQ8Cn6rykIFccyPgJcDtgN8OxOYqZu7k4/T5+5TfbXx8KeCbwMuAL1Wp3GvGQ2DoovR04DlL3PGm8vL65cBcFX9EaD8OfH7O9rsB7wSOBJ7bcpsuDLwUeDLwixaf9QDgmkVw9ytCc13g9BXPvBXwYuDhwJfLNVcDXg48Avhhi7Z2VfVFgA8BFwBuMQJRquLjCFJ+xxGf9wO/L+1/PvAo4AnAa7pygM/ZPoExiNKfAJnuyA/634C3A5/dPtq1LMjo6BPA24DD5l5KEYqI1JWB6wHfXqv2ajddGvgIcNsdBKJaTTtflRFuRkWnFMG9JbBKlK4NfAC4J/DpuWr/Cbh9+cI+sQmjtlzHQ8qHx2kjEaUqPk4/uwrwxgX2GQ1/DLgOcPMyE7Jl9/j4LgiMQZSOBr7bAqw/A34CfL9C3fnay5RhXoy/q3D9qkvy48tLN+3Ze24qK9N4+e83BvYBPrnBM3a7tStRmrfj3cAqUUrbZ1/QdypTdrN7M4K8cxnV/XS3hu3w9234etGc+PvqZYR/8ZGIUhUfv6GI0tOAzy1AeWKZ1s0I+Skb+NdbB0RAUVrtrIxUHgjccRdhiiBlWi0vxwjTJlNeeQHfvzwvayWzkpdUpjcuU74cv9diH+ubKN2siPDDlnxNN4VhG76et/1CwOPKCzjTd1MSpfeV387rgPh4vtwVOA44FrhHU862nn4TGJMoRRzyUv9NQ8hnYpMfxiphqnJNE+ZkfSGL+Vk/yQs08+5tlb6J0ovKSCjilGnZ2Hcx4NQSzNIEhyp+rHLNurZk7SWj7EzLfnRiopTAjkOAVwBfXwCYj8I3A5kNyb9bJkBgDKKUNZgbAFl3ybpSpkDSif+5Af/t9CJq8yU1b/oly/TVN4BHl6izBpq2soo+iVL6Z17S+wKJ3spI9OdlWvWAMs35woY+RLbl66wj5sV8TPHI1ERpVUeM798BxM93LyOmNvu9dfeEwBhEKWs4mXOereVcvowqMqUWcdq0LHtZtS1IGfHly/CqZXE/7cjLt4sQ4T6JUha7E+CRAIhEAyaqchadd17gXWXEFLHeZC1v1ke69nWi7DJtlxHwWYrSuX6qiczMGlNGkJm6a2oGZNP3gfe3TGDoonQF4EdzP+gZroSTZkogX6CJ7tq0zF5Wf1Wm8hKWvNO03qbPm78/U1VpT6bwEp01C4duHVnJyAAAG8NJREFU8hnzdfVJlDL6/QpwjfLyzhTPfEngQ4Ig9i/7lZpg0qWvDwK+AGQUPCuOlCAfHBk5ZhQZ3yYa0TIRAkMXpVVuypA/+3qyxyFfoU2U2cvqUCCBBglFzrpGFyXTkllPySbaRKllY+G6JSPJxwJpz7KSRfds3k1ofTYjLytZ03plxcjEKnauir7LSCkv7YQFR5Q/s1BZRlBfLSOmA6s8qOI1Xfg608zx5VsXbGpSlDLSzh6udX/nGaXmd9RE2SnCcrH+rJver3wAdvUba6KN1tEAgXU7awOP3riK2J7pj2RuWCzZjJl9LflBZW9LEyUvqmeUQIMsSHcpSrE/u9uzsTYhtBkFrlsibMmKEHbLShVRylTKq4EfrGvEwn2rXlhhno3EeXknZDoCNF+uVEbCEa6I1mwKbFOz2vZ1pmcT7pwPpsX+26QoZV9bNqCu+zsP16zrNFGqitJdSv8+GNgkzL8Jm61jCwTW7axbMPUPHvk84EllETRTOPMlKVoSWttUKOnsJRWBS+h3fugRvqaFKVkLUu9ry2hsvk2PBF5VQsMTidbWHHufpu/S/kzjZJprJ1HKlOZNG2LSha8jsslE8p0lP6RMV52/pM5KGqVEHy5GpfXh91fXhiqilD14GaUfvhDQk7RDClRd4gO9fsiiFCHKmsK9y1TTvAvSsf8eeAGQTXmblPmX1B1KxFfmvLPO06QwzS/q5ws6U4/zJYv5mTLL4m9eam0FPfRNlB5U9ielzfPZHMJmNn2XUXF8s2mofFe+XtUfZ5uk8/cxpBmab+duopSPjnx8JEBp/oMrI/pMmWemwDIBAkMWpbykM7WzbOE/X5eZosqIIgvl65ZlL6lZXU0LU+pLeHvSCGXfSkZ58yX5vxJgkbblS7Kt0jdRSjBLpu0yKl5MRZNQ8ROATPW8ZUMgXfpaUTo3gax9Jew7H12LU7AJcomfk5DYMgECQxalrI1kB3hGLPPhwFnI/5eygJw1oHW/nsMmiSKTvThTKstSGUVIIhLJ39XEVF5GeBdd8vJNJodkdEhm7EzxtRmNtA1Ryqg3I4PkuFvWtiOAvyyZs2drMPFPRGrP8rd/3+D3ug1fLzM30YZZx8mL+SYNTUdugKXRW1f5OHkrk+U/fXxZWH/26SWIJR8flgkQGLIoxT0J+U6UTlKRJCIto4zM1b+nTN1tsnclUwb5J9NCy+b+50dMEabMh/8FsElm8vgj01XZDPxe4GvAFUtm8ExjPBg4ueV+2ZUoJQIwgpKX0Q05Jww4bcv6SdZSIkTZKJuStmcvWmxLlvQIUHyTvSwPLdsCNsGyDV/P25uAhLQ3L+AkMU1J5FtSVj2roW0Nm/BZ994qPs4MQD78VpX8htNPvrWuEd43LAJDF6XQTrh00gBlfSFRcfkiSyLVTUtelPlqr5KQNS/UBFckcqqJCLCMljI6yzx7XszJlvzFhWSkm7Zv1f1didI69ierQ3wd3slkHibrjoTnn79NX6/DwXskMFoCYxCl0TpnSw3rsyhtCYmPlYAEuiKgKHVFejjPybpG1umynrbJVORwWqylEpBAbwgoSr1xhYZIQAISkEAVUcr8fRbbq1y7imjm/ZOaZ5PAA70lAQlIQAIjJ1BFaBJAkI1vEad1S0Qp+xAW08SsW5/3SUACEpDACAlUEaW+NPuZfTFEOyQgga0T8H2wdRe0Y4Ci1A5Xa5WABNoloCi1y3drtQ9JlLYGyQdLQAISkEA3BBSlbjj7FAlIQAISqECgiijlgLUkCk0KlHXLz4Bbd3Bq6rr2eZ8EJCABCfSAQBVRSvbkZGreJPouoeBJ15OcZhYJSEACEpDAUgJVREl0EpCABCQggU4IKEqdYPYhaxBI8tWjgPsCZyzcn9F7MkvfBrgckJNJkyU+B8HliA+LBCQwUAKK0kAdN1Kzc7hhjqPIWVk51Ten8Wbz9ulz7Y0gJS9fxCcZ4bMxO0dbJF9fjqnPib05DsEiAQkMkICiNECnjdjknCWUUdEpwDvLse+LopQDFa+y5CDECFiO+Ehgzs2Bk0bMyaZJYLQEFKXRunbwDUtqq1suGSm9oYjS04DPLbTyiWXKLwcCPmXwBGyABCZIQFGaoNMH0uRVovQ+4M7A64CHLbTlruUU4mOBewyknZopAQnMEVCU7A59JbBKlG4EHAK8ohydPm//A4E3A0cD+XeLBCQwMAKK0sAcNiFzV4nSKgTpy+8ADigZ6Y+bECubKoHREFCURuPK0TWkriglai9rTCeWqbvfjI6IDZLABAgoShNw8kCbWEeUkm3kGGAvYH/gtIG2WbMlMHkCitLku0BvAdQRpcOA+wF3BE7tbYs0TAIS2JWAorQrIi/YEoGqonSXEvhwMPDTLdnqYyUggYYIKEoNgbSaxglUEaV9gHsBhwNnzlmQtEMKVOMusUIJtE9AUWqfsU9Yj8BuorQ3cBBwJDAf1JCUQ4eWPHjrPdm7JCCBrRFQlLaG3gfvQmAnUbpqCft+JXDWQj3XAPYFXi9hCUhgeAQUpeH5bCoWJ9nqLYBrL0TT7QEcD1wGyDldiyWHUR4InDAVULZTAmMioCiNyZvDb8tjgT2L4NywHCx5csnckAMijygZwHNsxaoSoUod3xo+DlsggekRUJSm53NbLAEJSKC3BBSl3rpGwyQgAQlMj4CiND2f22IJSEACvSWgKPXWNRomAQlIYHoEFKXp+dwWS0ACEugtAUWpt67RMAlIQALTI6AoTc/ntlgCEpBAbwkoSr11jYZJQAISmB4BRWl6PrfFEpCABHpLQFHqrWs0TAISkMD0CChK0/O5LZaABCTQWwKKUm9do2ESkIAEpkdAUZqez22xBCQggd4SUJR66xoNk4AEJDA9AorS9HxuiyUgAQn0loCi1FvXaJgEJCCB6RFQlKbnc1ssAQlIoLcEFKXeukbDJCABCUyPgKI0PZ/bYglIQAK9JaAo9dY1GiYBCUhgegQUpen53BZLQAIS6C0BRam3rtEwCUhAAtMjoChNz+e2WAISkEBvCShKvXWNhklAAhKYHgFFaXo+t8USkIAEektAUeqtazRMAhKQwPQIKErT87ktloAEJNBbAopSb12jYRKQgASmR0BRmp7PbbEEJCCB3hJQlHrrGg2TgAQkMD0CitL0fG6LJSABCfSWgKLUW9domAQkIIHpEVCUpudzWywBCUigtwQUpd66RsMkIAEJTI+AojQ9n9tiCUhAAr0loCj11jUaJgEJSGB6BBSl6fncFktAAhLoLQFFqbeu0TAJSEAC0yOgKE3P57ZYAhKQQG8JKEq9dY2GSUACEpgeAUVpej63xRKQgAR6S0BR6q1rNEwCEpDA9AgoStPzuS2WgAQk0FsCilJvXaNhEpCABKZHQFGans9tsQQkIIHeElCUeusaDZOABCQwPQKK0vR8boslIAEJ9JaAotRb12iYBCQggekRUJSm53NbLAEJSKC3BBSl3rpmq4btAfx4qxb4cAlIYJIExiRK1wKOAu4LnLHgzccD1weOB04CfgX8KXAb4NfAs0fm/csBjwEuCJwJnA18EPhUhXbeCHgJcDvgtxWuH8olO/WP8wD3Kf0h7C4FfBN4GfCloTRQOyUwBgJDF6UHANcELgvsV17C1wVOX3DO04HnLHHYm8rL+5ctOvPCwEuBJwO/aPE5s6pvBbwYeDjw5fIfrwa8HHgE8MMdbLgI8CHgAsAtRiBKVfpHBCn9I+LzfuD3pf3PBx4FPAF4TQd+8xESkAAwdFHK6CejolOAdwK3BFaJ0p8AmZbKi/ffgLcDn+2gF1wa+Ahw2yVi2fTjrw18ALgn8Om5yv8JuH0ZCZy4w0MfAhwJnDYSUarSP+KXqwBvXOCSUebHgOsANy8j7Kb9ZX0SkMACgaGL0nxz3r2LKB0NfHcLPaArUTrf3Jf+ncqU3ay5dwPuXEZrP13BYG/g6mXkePGRiFKV/vGGIkpPAz63wOaJZUo4I8+nbKHv+EgJTI6AotS+y7sSpZsBnwQetuSrf7dWXgh4XHkBZ/puSqL0viLYryvs5lndFTgOOBa4x24Q/bsEJLA5gSmKUtYQMqr4zeb4KtXQlSi9qIyEIk6ZlsxzLwacWoI5djI2ay+Z1vs28NGJiVICOw4BXgF8fQHSA4E3Axll598tEpBAywSmJEqfAG4AJPAg60qZqsrL5p9bZtyFKMWPEZN9gUSZJarw58BPgAPKtOULVwjxXkBezMcUDlMTpVXuD9N3FH53LyOmlruK1UtAAlMSpd+VqLT8b8rlS4h0FvYjTm2VLkQpi/KfL0EeifJLVOEsAvG8wLvKiOnRwKz9aW+i7DJtl8i8sxSlc3WBRHVmjSkjyEzddTWybqsfWq8EBkFgKqJ0BeBHcy/emXMS9pupm4wUEsHXRulClDL6+wpwjSIymYqaLwl8SLjz/mW/0uxvBwFfAL4xd7EjJYiQZ+SYUWSYJRrRIgEJdEBgKqK0CmWmthJKnr0oGS2sUzLieiyQtaplJUEE9yoh6Nm0u6xkb8wrge+vY0DZnxVxSfhy9hd9ZqGehMl/tYyYDix/y/RlQujfunBtk6J01bI3at1+ltFf/NNE2Sk6c7H+w4D7AXcsI8wmnm8dEpBABQLrviwqVN35JateOmljpqmSuWGxZMNt9vXkxZe9PeuUbNxN9oQ8Y11RytTQq4EfrGNAEcSPF5FJaHcEaL5cqYwEI1wRrYhgwp0jxItcmhSlK5cNqOv2s9ibdZ0mSlVRuksZPR8MrAqfb8Ie65CABJYQWPdl0UeYq146zwOeBGSxOlNY8yWpdBIC3WbIbxfTd2lTppsyHbeTKCXDw02BG5cMF99Z4shMV52/pGRKeqJE9S1GpfXR/7vZVEWU9imj2sNLeqZZnUk7pEDtRti/S6ABAlMQpQhR1lTuXabQ5rFlWu3vgRcA2TzZRulKlB5U9idlSm4+m0PaNJu+y6jwDmWktKytCZWf3TuGNEPzbdxNlCLmEfUEvswHNWQEfGjJg9dG/7BOCUhgjsAURCkRZ5namuWBm+8AGQVk6i17exIo0EbpSpQSzJFpu4wKF1PmJFT8BCBTUm/ZoZFTFaWsfWUknXW9WRTiDFOCR8Lv9W10DuuUgATOTWBMopQRUb7uk/9tPloqaz7JcpBIu/lw6AQo/EtZ6H/GDqOHTftMV6IUO48A/rJk+J6tFcXHEak9y9/+fYcGJYov6zh5Md9kZGHQq/pH8iEme/xlFvrHDNMlgQSHRNQtEpBAywSGLkqJesvLNi+UG3JOKO/JZQ0k6yF5SWcTaUK+E02VlDE5kuB6ZU3lPWXqbl6smkbepShlqil52vLM5wIRoEw9Zc/NQ0tY/LL2JSAhrPICThLTlES+Jav5s1oMl2+a9WJ9VfpHMoDn2IpVJX0jfexbbRtr/RKQwPCzhNfxYbI4JMQ36ytJp5Mv52Q8aLt0KUqztiSrQ9oakU6G8i+2OBJsm5/1S0ACEyIw9JHSEFy1DVEaAhdtlIAEJPAHBBSl9jtF1mmynpWD5No8TLD9lvgECUhAAi0TUJRaBmz1EpCABCRQnUAVUcq6xBU3PKU2GQS+tyK6qbq1XikBCUhAAqMmUEWUEhiQjYcRp3VLRCn7QBbT36xbn/dJQAISkMAICVQRpb40+5l9MUQ7JADYH+0GEmiBgKLUAlSrnAQBRWkSbraRXRMYkih1zcbnSUACEpBAxwQUpY6B+zgJSEACElhNoIoo5eC4T5QUNOuy/Blw6xVJUdet0/skIAEJSGBkBKqIUk5UTQbqTaLvkj8sp6omH51FAhKQgAQksJRAFVESnQQkIAEJSKATAopSJ5i38pAkZT0KuC9wxoIFGf0mM/ZtgMsBOVk12dNfBnxpK9b6UAlIQAIbZmkQYP8IPKAcU5EzpPYDLliyop8+Z2oEKXn4Ij7JlJ6NzTnyIvn5HgU8AchxDhYJSEACnRNwpNQ58lYfmLOQMio6BXgnkKPRk5FjXpRuC1xlyem0EbCPAQlsuTlwUquWWrkEJCCBJQQUpfF2i6SGWiZKbyii9DTgcwvNf2KZ8stBgU8ZLxpbJgEJ9JWAotRXz2xu1ypReh9wZ+B15Zj4+SfdtZzOeyxwj81NsAYJSEAC9QgoSvV4DenqVaKUo+EPAV5Rjo2fb9MDgTcDRwP5d4sEJCCBTgkoSp3i7vRhq0RplRHpC+8ADigZ3Y/r1FofJgEJSMDou1H3gbqidM2yxnRimbr7zajp2DgJSKCXBBwp9dItjRhVR5SSreMYYC9gf+C0RiywEglIQAI1CShKNYEN6PI6onQYcD/gjsCpA2qjpkpAAiMjoCiNzKFzzakqSncpgQ8HAz8dLw5bJgEJDIGAojQEL61nYxVR2ge4F3A4cObcY5J2SIFaj7t3SUACGxBQlDaA1/NbdxOlvYGDgCOB+aCGpBw6tOTB63kTNU8CEhgbAUVpbB79z/bsJEpXLWHfrwTOWkBwDWBf4PXjRWPLJCCBvhJQlPrqmc3tSrLVWwDXXoim2wM4HrgMkHOuFsslgQOBEzY3wRokIAEJ1COgKNXj1ferHwvsWQTnhuVgxpNL5oYcsHhEyQCeYytWlQhV6vhW3xurfRKQwPgIKErj86ktkoAEJDBYAorSYF2n4RKQgATGR0BRGp9PbZEEJCCBwRJQlAbrOg2XgAQkMD4CitL4fGqLJCABCQyWgKI0WNdpuAQkIIHxEVCUxudTWyQBCUhgsAQUpcG6TsMlIAEJjI+AojQ+n9oiCUhAAoMloCgN1nUaLgEJSGB8BBSl8fnUFklAAhIYLAFFabCu03AJSEAC4yOgKI3Pp7ZIAhKQwGAJKEqDdZ2GS0ACEhgfAUVpfD61RRKQgAQGS0BRGqzrNFwCEpDA+AgoSuPzqS2SgAQkMFgCitJgXafhEpCABMZHQFEan09tkQQkIIHBElCUBus6DZeABCQwPgKK0vh8aoskIAEJDJaAojRY12m4BCQggfERUJTG51NbJAEJSGCwBBSlwbpOwyUgAQmMj4CiND6f2iIJSEACgyWgKA3WdRouAQlIYHwEFKXx+dQWSUACEhgsAUVpsK7TcAlIQALjI6Aojc+ntkgCEpDAYAkoSoN1nYZLQAISGB8BRWl8PrVFEpCABAZLQFEarOs0XAISkMD4CChK4/OpLZKABCQwWAKK0mBdp+ESkIAExkdAURqfT22RBCQggcESUJQG6zoNl4AEJDA+AorS+HxqiyQgAQkMloCiNFjXabgEJCCB8RFQlMbnU1skAQlIYLAEFKXBuk7DJSABCYyPgKI0Pp/aIglIQAKDJaAoDdZ1Gi4BCUhgfAQUpfH51BZJQAISGCwBRWmwrtNwCUhAAuMjoCiNz6e2SAISkMBgCShKg3WdhktAAhIYHwFFaXw+tUUSkIAEBktAURqs6zRcAhKQwPgIKErj86ktkoAEJDBYAlMSpbT10sBPBustDZeABCQwcgJjEqXLAY8BLgicCZwNfBD4VPHhhcr//yJwxg5+/Sxw/Mj9bvMkIAEJ9JLAWETpVsCLgYcDXy6krwa8HHgE8EPg8sD/A1x0B0/8CrgjcEIvvaVREpCABEZOYAyidG3gA8A9gU/P+eufgNsDtwFOBG4GPBr4UBlFLbr2OsB5gKcCvx+5322eBCQggV4SGLoonQ94fxGROy2Izd2AOwNPBn4K3BvI1NzJSzxxEeAFRZAy9WeRgAQkIIEtEBi6KGX080ngYcAbd+G3P/B/A79euC4Mng4cB5y0BR/4SAlIQAISKASGLkovKiOhiFNGQYmuuxhw6hLxWeX0/YArVhA1O40EJCABCbRMYMiiFNs/CuwLXKusHf28hHwfAHwXeCHwmx0YXgp4XonaO6tl1lYvAQlIQAK7EBiyKCX0+/PAdcto6U3A6aW95wXeVUZMCW743QoOEa1M6SUowiIBCUhAAlsmMGRRujDwFeAawOOAVyywTOBDgiCylpT9SovlKsA/lBHW/7tlP/h4CUhAAhIAhixKGSl9AUgo9y2Azyx4NCOor5YR04FLvP1/ATcHIl4WCUhAAhLoAYEhi1L2FH0cuCWwdxGgeaRXAk4pwhXRml8ziqAlMOLDwBN74AdNkIAEJCCBgY+U4sBjgIN2EaVkeLjpQsDDbBT1eOCv7QkSkIAEJNAPAkMeKYXgg0ood0ZL89kc8reZ8CTbwx0WsjQ8EHgz8GAgARIWCUhAAhLoAYGhi9IVyrTdk5bsM0qoeHLYHQy8ZYH13wKPApL14T098IMmSEACEpDACKbv4sQjgL8Ebje3YTZimwwPe5a//fuCt98N3F1R8jcgAQlIoF8Ehj5SCs0LlAzhyebwXCACdChwTeChwI+WIH8HkIi8RN55TEW/+qTWSEACEyYwBlGauS9ZHXLsRDbOfgTIuUmrsn3vVTKIv66cvTThLmDTJSABCfSHQBVRyks+ueGqXLuqZRGH7+2QWaE/RLREAhKQgAS2RqCK0CSKLWswEad1S0QpazjZzGqRgAQkIAEJLCVQRZT6gu6ZWzRkm8/eYrN9tAQkIIFuCShK1XgrStU4eZUEJCCBjQgMSZQ2aqg3S0ACEpBA/wkoSv33kRZKQAISmAyBKqKULNyfAC65AZWfAbcGkofOIgEJSEACElhKoIooJRt30vlsEn2XQ/a+D5ytHyQgAQlIQAKrCFQRJelJQAISkIAEOiEwRlFKZoejgPsCZyxQzKjvPuW02csBlwK+CbwM+FInxH2IBCQgAQmsJDAWUXpAyXV3WWA/IIf4ZdPv6XMtjyA9vYhPjknPht7kzXt+yRj+BOA19hUJSEACEtgegbGI0vXLqCgnzb6znEa7KEq3Ba6y5IiLCNjHyrHqOR79pO25wydLQAISmDaBsYjSvBeTEimH/i2K0huKKD0N+NyC23Mkeqb8Xgw8ZdpdwtZLQAIS2B6BKYnS+4A7A8kM/rAF5HcFjgOOBe6xPXf4ZAlIQALTJjAlUboRcAjwCuDrC26fHY9+NJB/t0hAAhKQwBYITEmUVuENgxz6d0DJZJ4Rk0UCEpCABLZAQFE654TarDGdWKbufrMFP/hICUhAAhLY8OC+vgJcFeiwzN5kqTgGyEm0+wOn9bVR2iUBCUhgCgSmPlI6DLhfOUb91Ck43DZKQAIS6DOBKYvSXUrgw8HAT/vsJG2TgAQkMBUCUxWlfYB7AYcDZ845O2mHFKip9H7bKQEJ9I7AFEVpb+Ag4EhgPqghKYcOLXnweucoDZKABCQwBQJTE6WrlrDvVwJnLTj4GsC+wOun4HjbKAEJSKCPBMYoSkm2egvg2gvRdHsAxwOXAXK+02LJIYYHAif00VHaJAEJSGAKBMYiSo8F9iyCc8NyIOHJJXNDDhY8omQAz7EVq0qEKnV8awqOt40SkIAE+khgLKLUR7baJAEJSEACNQkoSjWBebkEJCABCbRHQFFqj601S0ACEpBATQKKUk1gXi4BCUhAAu0RUJTaY2vNEpCABCRQk4CiVBOYl0tAAhKQQHsE/j+MOzhogSUcBAAAAABJRU5ErkJggg==)
Question 2.Choose the correct option and justify your choice:
![](data:image/png;base64,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)
A. sin 60°
B. cos 60°
C. tan 60°
D. sin 30°
Answer:(i) We know that,
![](data:image/png;base64,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)
Putting values in given equation,
![](data:image/png;base64,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)
[Since, √3 × √3 = 3]
in options we have,
sin 60° = √3/2
cos 60° = ½
tan 60° = √3
sin 30° = ½
Only (A) is correct.
Question 3.Choose the correct option and justify your choice:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIYAAAA2CAYAAAACs+HkAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAARnSURBVHja7ZsxUttAFIY3fegD43UXerymDJXH0WSgpDAadwyFhtEMgRkVLmR3LnIBUkGZE6SANgU+AQWcwD6DiNbWyossaVeyvLsyr/gLsMHS06f/vV3rR6PRCIFASUERQAAGCMAAARgVFAGhT7ygJgAGGo8vPlsN9BgCESyEpx1n0AIwPngBfL+/S4jts5+HNjlGDevxYjz+bKKjGQOGLnvVZekDp9PC2PqzLhiiuiXbV1Y7m4MauxkKiD081g5GbLPk7F7lxYmK8aaqCEye198jCD9Zrn+w7v86I+g+6xy49vWWqqjevmsdYNSa9H1/l7lbC+FJFcdXCgxKrOdd7JxZjSF/oNsKBj3fxWeSF3YR1tFlF9+wiywBRrAiYt/FdUjUngKnoi5IimbFYPg9cjIvas8/SbNXkf1mtaSs987v7vAcq+jlERRBu92+FYIhmGVix/C8vcXN2t/T5hjzg8bogSNYKRhhYa/z7bX3tY3xX4zQbPk6njXJ99+nzmB/9X/hWcdxjnoW+Rn/DW5N2MpjUXw0Td61Ze5KBjTuXl7nuZ4sGMbOGPOJHaFXDWAEKzYb2WvWhVyIvPKtIAFZ8A72xHsrGVopeHwbkAHD83ZM3EMxDowiMwZfUNbX+b+JwcDkybLdH+yi5A2G5YfWsE7YemAOIAVGwhXTXA/AKAAGHYx73e45bSmNRuMfX9xVMPAs2ZMj15lRy69sgyxx9yfnJEG75pxs9XhrD4ZobS5rlXlgxJadPtErB4Mdq0gid6KzUwSL8mF/42DYBN2l9/6lZC5GFhi8BTfb1m3PdQ9cd/iFv9iawMg637ciQ2NcbwN2XmvVSvKOhzmJajDKtsM091wOsIY6BrP9eKji1vgqwaCf+65vMzDCFQUd0tjvHee0RecNHa2kDBj0NTZosnMYOKf7IRUTttw1DgzRdq2KdXQEwEvaPkZiObtcijabz3UCI+UcFufBrWzMAyN9Yla6weL3rKNmEz3Hswmxf7HX3C45X+5l4OmhZV+5bucb/V0KGNMMMKYKwAiylqu2dXjFnx87D1O+1TViMwVknqAIIAADBGCARuttOEIBt1jrbDhCAUFyjiFjPyBzpKyViKwHZJaglYBgVaJzcgcoAAxIoVUBhso7StXnbCqFJnpqvcgwqMvNit1ZCp4T0BU2oqoqhZb1TKls0ChRC+VfYArB0BE8qnsKLS9sJBs0mruZxhRaLhi6gkeqw0ZVptBEYaPCeRJNKTQxGIqDR6rDRrHtV5BCkwkbFQFDZwpNesZY59lPWiTZB2JUh42qSqHJho2KBo2MnTFUg1Fkxqhj2KgOQaPaglHnsFEdgkYbAyM5FNIihRfhRnaH8aOFjUwLGm0MDJkvbvhlmSwY2xw2MiloVLtWsi1hI9ODRtIbXOsGj8qCsY1hozoEjcptcJUIHhUFY5vDRnUIGpXZ4Cq11i8KxmKzaDvDRnUIGhWaMUAfT1AEEIABAjBAAAYIwAABGCAAA2Sg/gMYcLFJY8UAgwAAAABJRU5ErkJggg==)
A. tan 90°
B. 1
C. sin 45°
D. 0
Answer:![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAhCAMAAAD03JuvAAAAAXNSR0IArs4c6QAAADNQTFRFAAAAAAAAAGaQAGa2OmZmOpDbZgAAZjoAZrb/kDoAtmYAtmY625A625Bm2/////+2///bgeJ6FwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaklEQVQ4T7WRWQ6AIAxE676h9v6nVbSoZQwkoP2clynLI0oYnirdkmCuOw3uwHgNckEYrG1xTL+fF2vwWC7qWhIYu6B5EAgSviC3cj4LJ3fvb/24cx6sJULnAtDgOwg59xuXcwfAuYDPnW/ETgP1V49luAAAAABJRU5ErkJggg==)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAA///b//+22////9uQ29u2kNv//7Zm27ZmkLbbZrb/Zrbb25A6ZpDbOpDbtmYAkGY6Oma2AGa2kDoAZjoAADqQZgA6ZgAAOgA6AAA6AAAAe3bfNAAAAAF0Uk5TAEDm2GYAAABgSURBVHjalY5ZCoAwDAXHqFXrWvfm/gcVW0EQBJ2fIY+QF3iSDOpboBnTbDfIZkmmDlkN9OPtK6dfwh4yq6/5jEb4TT6rOpC1ovQmRKH/fLkLKl2cogoHhUW2s86+XT0ApMgEvIVNFocAAAAASUVORK5CYII=)
= 0
Hence, (D) is correct
Question 4.Choose the correct option and justify your choice:
Sin 2A = 2 sin A is true when A =
A. 0°
B. 30°
C. 45°
D. 60°
Answer:Out of the given alternatives, only A = 0° is correct
As
sin 2A = sin 0° = 0
2 sin A = 2sin 0° = 2(0) = 0
Hence, (A) is correct
Question 5.Choose the correct option and justify your choice:
![](data:image/png;base64,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)
A. Cos 60°
B. sin 60°
C. tan 60°
D. sin 30°
Answer:![](data:image/png;base64,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)
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PQCJSJ6EosUmybMLFtnQgrahlAlLEQEZMIWCx6ecIVNMnadZvAPALESONHlJRqLuMmUFagOV2f0/WN5ZthgTaWmfQ47kSAtyCsllUOryC4Od4/a+vcyE3ABJojUFagOV3fPwwFTaXr8+9qc2s+W7MFWnus3VLLBPAj5EeeH5SyhR86Dp8Q4NfFBEygPQJlBVrSw3mxLJ2ur9xc+ne1HLcydzUm0A4s0xvfYwIZAmNYR2MYgxdm/QS8LhZn2rRAc7q++td0mzUO8ftTtM8WaG2uKLdVmEDRBV24gRZuGMMYWsA0uSa8LroVaLTudH3D/doN8ftTtM+NCbThTrt7bgImYAIm0DWBpi1ojM/p+rqeZbe/GAELNK8PEzABEzCB3hFoQqA5XV/vptkdWoSABZqXx2gJEEiYHIwEKi5b/jdSdF1RtgLfZwImUIpAEwLN6fpKTcUdbvLvanWGeWuwQMtLytcNjgCRxB9c8RQn4TWIb+dI84Obfnd44ASqCjSn62tmAYz5d5VsPpvUhK2ov9msZi3QapqMvlWzXGQG+JOkKyX9uW8ddH9MwARMYBECVQWa0/V5eRUl8LXIvU1Gn6rFAq0qwRHeT8yvXSJt1LcjwfSOksgHelwq08EIh+4hTZgAacqOkLRdZPWYMIrRDL2qQHO6vtEshVYGspqkCyK4+V9aaXF+I7agzWc0qCteHjlHSSqdlK0iNQ4m/48PajTurAksTID1TP5bcnRuJGlpSVhNfmNooyBQVaAlEJyubxTLofFBkHObnaY3Nd5S/gYs0PKz6v2VWM9Izv4tSe+UdFv0eBlJWNP+KIk99uTvvR+QO2gCixB4fFjLfirpNEnrWKCNar3UJdBGBcWDaYTAPcLX+MmRJL2RRkpUaoFWAlpfb8GCQMLzh0WC91+mOkoy9EdLWrNnFgbiECEs8ZVzMYGyBHiY90Gg2fez7Aze+T4LtPpYuqbFCewk6cWSnrfAZRyMeEk8QwlufO+w3J8g6SsNwrVAaxBuF1UjwJaN8BJJ+7wdXCbpr5LWltSH/XWsehx5v290ki/AQZLSorILfm5zmAS6Fmj2/ax/3Vig1c/UNc4mwA4Tzx92oLIFX8bXS/pGPEeTz18YlvsDJB3cENjOBJqdehua0RnVPlXShZLeHI7URVou8+aASMRZe0kcSiAOGQvtqlTDHFxgy5WtKQrrYU9JuxXpnK81gSDQtUCz72f9S5E5PVfSlyPMzc8d7qZ+yK7x70YL1ho7T7PCKbHzRDzNkyXtHYYOsCWGj4fGzlQdJz+p9+6SVox5wVXpq5KOr2OeUJqLlSk49T4//L1urANoDXWwhXiGpFskwb+I9azMm8MzJL1LEm8Xv47+s9joA4v74vgbAg5T8cfi/x8naWdJr61hzK5iegS6FGj2/WxmvTGnW0bV10haS9KtzTTlWidMAOPBdYtYwfDb5rn1s1iDvw9WPL/4O35rzwwjSB0YMXB8L1XRq9sSaFNw6sVK9YmYzDomq2odiCJEE+LsDwUrK/rmcC9Jl0jaT9LpmbbYv+fvLHb6sZSk14VTN8FgWfSHpkRdwa768okT6FKgDdH3c+LLxcM3gb8TwGcUyxfPuoWMKgixl8Uhgi+luHE6+HJJy0siuwIW3l6XeRa0dOe7/EFtCiLbgZ+XhOJFbXddcHp8lqQ3lnTCL/rmwNvuSbHYib6fLpiP2eIk5MfZqQ9YM/xzpP6uV8uw2+/692Qovp/DnmX33gTqJYBv2dPjAEDRmrnvIknvjd2h24tW0Pb1Uxdo7GWfL4mAd10LtHUl8Y/tRixUFEyxmE7zbnMWfXPAcshJOh5WbKmmCwcXvi+JNxC2Ml2mQ4C3S3y0OBTCQZUmSpMC7SGSdpf0XzPW9WJjqeL72QQj12kCJnBHAhgNdpVElIMiBb9qDA1XS9oj/KmL3N/JtVMVaJg615f0wcj9iCXpVzEDnEpkfzspWNk2lcSPPlajB0UQWcRLunC6EX82cklS/+GxNUjdmFT521mRxik72fhqYDk7JmOZYkvxAzU8JGe9OeCHw0EEtjmfNCO1FA6ViEO4IBxtMevkK9p6o4iUfcKqnPhuNNGJJgUa/X1KjIMsHXnGUcX3swk+rtMETOCOBJ4Tz0MMKnkKBgsOt7EbtHXsFmEAaeqlM0+fCl0zVYGGIOEU4rMlEU8Fs2kSzfxHcWgAkIiYN0g6J+UEuLKkL8RCQVAlBRH2AknbSmIhIbqeK+lTkn4h6QlxH+1RX1IeHicmSVmRLggnToeg9quUhd4cEgHGwwsBl120yeeYgTkQYGfff83CWE80sxY/GY7eTYdPaVqgMVtsz/OC9IocVugqvp9Vvp++1wRMIB8BIggQOuOofJff6XmKzzTPuldKuqJEHa3fMlWBloB+laQPSeLY7awtztVDmCGycDpM9qz50ScF0xMzoSiolxQ2X4wYLah1QlMkBX83HJQRbtTFWztB87CezSo46ZeJ15LnzQHhhhUQR8tZAi058cJ1Po31j0MbY05TxCEQYgqdmAql0uQPUhsCDes339NLw+9kofFU9f1skpPrNoGxE+D5x3cVd6OFygNiexIDSR6L+Kx6iOXJoThSzeHaw0njXhcLtMUFGtuaBMTD4oVPTiLQHiHpWknbxwnQ9CSz2MirOSuPJseDsd6x/ZLXr6zqAsISN+vN4X6SfhAnWSzQ5lMe+4lmLL+ETFmvpbXZhkBjVsn1yYsR2/SkmMqWOnw/568eX2ECJjCLAK5GRBDABxqf68TVKHvt2yUhzqr6Qx8ZO2Y8i6vW1fiMdinQ2BfG2a9IH9JAiLSfBE0tC2qeBY16sSThtI8447/xNcOJ+mvhp5MNSJcINB502W1LFgWft22RmvXmQOoLLGh8IRbb4oRB2/0tO59t3deWuGhrPFjP8Ed8fyrOXdNt47DLusNKfVODjfFmju8nLyP7Ztpp2vezwWG5ahMYPAFcgU4N/zAMFxtE6qbs6Uq+wzdI2jxSI84bOC9d7GQdNyOUBoHVcU0i3Ab+tm0ZSub1eebnRcRR3Q8lthVfU0GgYdlicquUPAKNbcht4qAAi4RAd38Of7JZAen6KNBglH1zwL+NPKAUtmqzuTUTHzT+zpsNY3b5B4G6vwtdc8Xcj18lLx7ZcCt19o3ME4+MQzOsOXw8OZCD3yeHUPaPbBZ1tkldBFmmbh4CyWnlpn0/6x6D6zOBMRHg+4eRBed9Iu+jRdipwqhxSGagW0h6a+w8zWOACxH1YjknnMZemRvw6T463B743ev1gYEuBdo80G18PkugrRKB8LCa4X/12bCgvTQVlJWtT7ZL+ibQirw53BZWQMaCJSHtKwd7LGyc4vxxvI30PmZMGwsm2hibQDssAhKz3TDG07p8p38Yh3dIAdOU72eLS9BNmcDgCfC9xFUoKRy0w/CC6xCHAZJC+rBTJH0kx4h56eM7Tugo3IyyAdiPlcTJbn7zshb1HNW3e4kF2p190Ij9hPLm1CJhOBBmnGJM+69kBRo+ZTgfUrqyoJV5cyBvGCKVU4nZvf8Hhjh7tySSy7r8i8CYBBrbB7y1cqqJ2GFjLFiD+eH/aPwwj3GMHpMJjIEARgYO9rBrc7MkRBzP1pUKRBIgC84948BTmgkCkK1NjBG006RrRS1zMXWBhsImtyTOh4kAw1EalY0SZwvwdzPigLFVghk1saBhNsV/p0uBVubNAcf3b0VeMk66pQu5ykh6zD59Os9YLQtv4JWMSaAlvojvkfS+gc/LQt3nd47AlpxY5oXLxQRMoL8E2M4k3eFm8UKF73d2q3Kx3vN9J7QOoa3ODP9TBB4REfC3JdRVOtZpb0kUEWhtOfW2CYt9aoQJ8csQIywEnAjZo8aywJjxy0GQoeYpCCGsTsRO44BA4tvFA47yvPDnweExG+2YyP2kY2JLsWiezTxcir45MEYOLtAXhGmyjcm6IPwIY+Wkyxi3vfLwXOiaMQk0rMHXh58W2wjZcmAVUB3dO6vPzBknl4l96O36jibGzZpADgI8lwhVRTQEnrP4ipEBoGjBirZxPG+XRH0YXQbzPJsn0Lpy6i06EWWvZ/zkvSQOEtYDTpbic8aJLwqqG8sYDvVJcDxiYREXjRMo75B0csSPYouQ7UDuWUESgT5xuMa6hjWK4HjUz3YLyV45BZp1hiw7juS+Mm8OWFCwGH43xkodZDBg25MtLxa2yx0J1C3QujzRzEsKp3lfGGt/rALt02Epn3Vi2evbBEygXwSIVcZ2JL6jG/ara+31Zp5Aa68n3bZEGqZVI3DdLEGCiOHUKQHyEF3JGzjmUtR4306CFH1zYB1wqg7RyeEILH/JCc9uZ6afrdct0Lo80TxPoPVzBor3ijmDswVacXa+wwS6IMChJfzGeLmaZLFAm+S0e9AVCdQt0Cp2p9Lt87Y4K1Xeo5s5zUUMQ29x9mhS3BUTMIGFCVigeXWYQHECYxJoy8YWJz6UnF4eY+F3Dn8WcuL6kMAYZ9hjMoERErBAG+GkekiNExiTQEvCbFwZ8YEahxcHZTapqaE8hxjIpMGWPQdiDq+pXVdjAiZgAo0SsEBrFK8rHymBsZ1oJmgjB1mIDYQPYtOFAzKEteGwTNWSR6DhX4oAZXxJvMKq7fp+EzABE2iUgAVao3hd+YgIjPlEM47zX4q8mD9reM5Wi8C4nHZuKw8eqZ7eFsEvsxkzGh6uqzcBEzCBcgQs0Mpx810mMCYCSbJ0kguf0PDACGdDXtc3NdxOUn2SLP2bkv6zpTbdjAmYgAlUJmCBVhmhKzCBURAgaTExAdnqREA1UYgBSJga0ri0Fcl7dUmfj2CXxCZ0MQETMIFBELBAG8Q0uZMm0DgBrGgcfjg1cuE10SApVggKTbaNWQVrF9kwHh1ZPYg/SMBKrHpfKdEh6iOvH8mTyavrYgImYAKDIWCBNpipckdNoHECDw+BhjWN9E91FxKWHxSZN7J181tEWpdvRJ7b5HMyHJwm6YDIpVekT1tK2iry8rXl71akf77WBEzABBYkYIHmxWECJpAmQN7ZN0e+WTJn1FXWDgsdaa1m5cLDaoali9Rpe6eyc7AtellkAVizwMlPxoGf2y6RAaSucbgeEzABE2iFgAVaK5jdiAkMigBi6RWS9qsxjRkxyPA7O3gBEk+TdLEkTpGulRJVd4u/47eGf9yFOUiSHWE3SYc6l2wOWr7EBEyglwQs0Ho5Le6UCYyKwHJh+UL43bjAyBBiL4tDBIT8SAp5ckmaTE6+NST9fFRkPBgTMAETWICABZqXhgmYQNME8C0j1hoHAIoW7rso0lCx9Xl70Qp8vQmYgAkMkYAF2hBnzX02gWERuErSrpLOK9jt+0gia8PVkvaQ5CCzBQH6chMwgeESsEAb7ty55yYwBALPkfQBSWQQyFPY6txREocJOE16kqR31egLl6cPvsYETMAEOidggdb5FLgDJjBqAoTIIHTGUSVGea9w9Geb85WSrihRh28xARMwgUESsEAb5LS50ybQOYFnSSIQ7PmL9OQBsT25coVQF8tEgnMC1q4j6ZrOR+4OmIAJmEALBCzQWoDsJkxgZATWl3S6pFsibdOvFhjf2yUhznauOP4jI4gtoTqq1lWxK77dBEzABNohYIHWDme3YgJjIYBPGemg8A8jGOwGkbope7oS69oNkjaX9J0cg19X0kaSSNieDaVBTLNjItzGUyU5K0AOoL7EBExg2AQs0IY9f+69CbRJgFRQRPVHnH1VEr8f50i6QNIhmY5sIemtkp6So4NLR72PjXAae2Xu4QTn0ZIujW3Ov+ao05eYgAmYwKAJWKANevrceRNoncAqkq5NtUoAWXJsbh+HAZKPzpV0iqSP5OjhXSPNE6mcdojt0/Rtx0bKpsMk7ZujPl9iAiZgAoMnYIE2+Cn0AEygcwJsT348/NFuloSIu0TSSpJuzdk7gtjeU9KJmesRgGQSIAYa7dyUsz5fZgImYAKDJmCBNujpc+dNoDcE2M58hqTNJGHpIp5ZdqtysX8HAboAAADkSURBVM7yW0T+zydIOlPSD0LgkbtzKUk7RS7P3gzYHTEBEzCBJglYoDVJ13WbwHQIcCjgi5K+HicuCYlBBoCiBSvaxpEwfUnUxyGDvxWtyNebgAmYwJAJWKANefbcdxPoFwFilbEd+UNJG/ara+6NCZiACQyLgAXasObLvTUBEzABEzABE5gAAQu0CUyyh2gCJmACJmACJjAsAhZow5ov99YETMAETMAETGACBCzQJjDJHqIJmIAJmIAJmMCwCFigDWu+3FsTMAETMAETMIEJELBAm8Ake4gmYAImYAImYALDIvD/hgqC2xt4aDkAAAAASUVORK5CYII=)
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vTQbulXDUnLK4oieObqUrJuQ+UdnVrjsAaks6MolSdPK50Ggpr5M29JNOetHXUlOdwi9Q2iRKdnOjG8ZZuJtA0Ad49ziKg/vu6kjjukUIgv296IAN+HkL8jSGwOdSJYkaUit5H0s5x+h1nLLg1Q4AzOq6T9LpmHlffUyzI62NZpSe0cQ5p4ZhSzh1Px7neOrRzzpDGZ5M/5rXKs3yPCZQhwPG5nEeAmfHjcRqbBXkZgrOv5dwEjl0+MncpmyY29gSV8f3H1ea2WAJYRImteUQfj/u1IF/syzGrd76wHHzCSWoc9MIpa6lxKMrqkh7cMS1omQhGw5fvNg4ClM3lWFUL8nrXm+OJEeR7xBHM2d5fHe6M/fuoIdaLqZHeto2TMzm6elLDesJxp/wmc0Q2h29hrTpC0pcaGeESD7Egb3sFbhDUt420qzQadoffjpPYHimpC/4arAT84ODDo/Fi753bfLRP0yNYBAEL8kVQlT4taQNJh0vaPveIjSSdIulkSbja3BZLgPgkfs+wkOYbcvJVkr4ev8vp7xuHtWpPSW9f7PCW7r2MIHfAS3Mr9WhJZ0l6fezKyzy5ys6RzQSBTBz7ip+OPG60hR9lHkwAHqZ+zKw03odXSNqpzOB8bS8JWJAvZtnWkrSdpIMlXZx7BN+3oyQdE8GvixmBe4UAyhLvOJbRSWmraOHUtzhe0m6Zo66TwsWx2PyG1hHpXmlFZgnyMQS8PCv80VdUIlj/TZiu2Yn/VRL8y2jjVXaORMnvK4nd5e9iOkTPMgZe2nPiMwQ9JqWj4/8fGj9CL68fgXvsGAEL8mYXhO/xiZI2jZP8+C66LY4ASsvPltCqiVPgd/BySQ/JZG7we8jn+NXXCeVrcaNcoudZgnwMAS9ovcfGIrWyCLmHIjwRrgjxa0oOqOzOcXlJ50p6U5jwso/DH8TnvMSMg2jaV4aflKIrBEIRXZuEf8mh+vIeEbAgb3axyBY4L1KhMKuX2cw3O9L+P436HWjS/HZOU+YQ2FtGMNzpmSmvEBkHd4rAxF+2hWOWIM+Oa4hfZszQnw3/FLuttttmUV70tZKqBJOV3TlybjemO15iIjazDTMTpnV+SEiNSY13hn+unNb229Lc84f43W+OXrknkclyXHwn15N0ZbnbfXVJAvi+145AtpK3/ve+syW9J6yXuCVbaWMX5PhGviaJQgBtC/LHS+IfZm40Xhomm++X2JGX3TliiSAaGf8OpvxsIwDvB5LYgeLHcxsvAQvy5tYei9wWktZfQkNsbjTDfxLKyo6SyBIq04gjQsH5saSXRfxQmftrvXasghyTyJMkvT9qe6OZ/jbIkgKGvyQ1tHa+VCuHFnr3KNaCkMs2ornxt1MrnP5JG8EkTd+YXviMKNVJOaH4XZ4g6dCcposp+32Z4Iqqiz9p58jOn4A6zOsE3VAIIdsI5GATARc2GNbAq9Lv/30W5M2s4YaxaaZI1NXNPHLUTyGPn99XFLkiDUWJIESslc8LayaK1z+L3LzIa8YqyBFcRF0/WRL5g5hXUsUqokdJRaAh7F4j6XMh1PiMvM/T4gVA8KaGsOaLSLlFXhCE89MlfUzSryWtGffxPPpLbdWIEKc0YLYhYG8Zu7153oFpO8ckqPF1I+jzL2P6O+YiAtuunWcQA7t3bBkcFuSLf4EJliIuZfecdoeCYKG+GP5k4JBSRtZA2cbvMzFC/Ha+RFKrpy2OVZCnRXuppA9KIn1gkmn9ASHAEcYEOyQfCFo2pVMfnkvRol/KWX4hchLZrZGylRr+eIrAIODpiwh1igmgjU9qBJtVyU8ssnNEwGNVIMBjkiBPEZlcx6Zk7IJ8DBkc037MLMjL/syXu57v1+aSyEfOBrYRYLpL1F0v1+O4r+b3FEsqbtNp7a5hFkcxQ5mp0qitQbAwhWFwUVIjv5VmQb60IMecjnaOBo25Kwnye0v6afiy8DNnGy8R5RUn1UknzQFrwKNK+L3nfTGm7RzvKOlCSURaWpDPpjyGDA4L8tnvQd1XYKZFMThkQilmqj3iAqR6mFsxAvCiiA4xP8QYJZdp/u43h3V13vgfDrfBostv+7x9FZvhhKvaFOS8wAQZlBlDdgpUPkvFSaoCmKWR0y+aKcFnCHH+G1MXNZA57o5qTFRlmiTIOc0oby5nsRH0TWu4k3aOlBhEI+dFX8q0ztyaHm/V9WzqvrFpqAT18I5goXIUdX1v2Z3D3YZbLgW4ZnvHGkYmS9lArPpG2K+ecGmSf4//GoXpKZIouZqPJkdbv0zSc6JE9qxZEiOEpZXTKPMpZhTEwsXKSXUU8molVbCMEK37xwtzNif8lBlDFjiaMos2TysiyDF/Y/Yi4I3FpwAAgWH4yfsiyGGU3znif6fOOw0XQT7dLfnI+ZydbT4Ybh7ufb+37u9CF3lQtW+1CNTk/SBehCBQYkgIfHxLVALs4tj7MiasecTUTGsId9bg0r5MqMVxEmuEcocQ/3LIFSypKFPvyI2L8rdvCMvorCHjCqVfzhkgzWzX3A1ErGNNIe8f83orgW9lhOgQf7wmCfL7RIEAvkTsiD8Zu+UXZIqfYHLnVKiuCfIyO0dOVMOqwFzQuLO+fN5VNHai1n8Su9HWciRnfdNa+PsQvwstYPQjTaBWAvx24/JMDUsHCh/pfAS1pfZ5SSdI+nCBp7OBpTwrKbq4SzHbZxvHzO4gab8IVCzQZf2XWJD/r4+cg0HYeRHcRXoaApyobQR3anlBjs+boAda8pE3bVqvsnPk6FQ2M0Rh531Jdwsh/q4Iwqn/7etvjxbk/V07j3xcBFBuCEzGqniVJIQ9v9UrlQjgJZtguQnHzbJRwKSOEsRzWnM7jV2Qs8OidjiRi0lQUzucXRY7MUzPf5iQR43/BXNL0sgxr7y3ZUFeZedIABdnoZP6gmko2/jsi+H3QTN3+38CFuR+G0ygPwQwo1P2mpPm0JyJdcqbyJeaDXJym0ghPjWChNkIkFFEZgEpxdnaI42TKSPIhxjwgt8DAUb+N0KLBSZ4AZ8HARHMmcA2BDe7ORoCEy2WSEUC3ZLv+d3xd4Ir8J8TaJEPUsEnRhlVTNll66gXeTnK7hyZIwF4jIUNTDKf816QlsdcicR0MZgb0x+SIN+ryItV4pq6+yvx6E5fWjeXuvvrNLw5B8fvHCnBZBPxu40vm4psZRtaOWVz+f3mpEj6Q9lr/fdxliAfesAL86euOZGhB0XFHnzipGXR2HWhaRMYlooGcKABeeVESL41jrbjDFtM05ihuYdoVCrEUb8cbR3tlqIBROoTREaRfvzT+SCMsi9W/voqO0d84VggvhdzpQ8qymFuJ4eVF9ZtsYK8zQyOugVC3f0N5d2rm0vd/Q2F87R5kOuNGfyHkp42tMnOEuRDm++0+VA+lZxNEvonCS6EHVH2FA5AOCfNFbMKu7FWIhWXWJyyO0feAyKT2ZwQ5IclIUW0j+UdKDPPujXyLmRwlJm/rzWBPhIgxxy/9kl9HPxSY7YgH9qKej5NEKhbkDcxZj/DBExgoAQsyAe6sJ7WQglYkC8Urzs3ARMoQ8CCvAwtX2sCNxCwIPebYAIm0BkCFuSdWQoPpEcEhpjB0SP8HqoJmECWgAW53wcTKEZg6BkceQqk7JDOuHqkZRLwSeQvB3hwYp9bPQTMuR6Oo+7FgnzUy+/Jm8BEAvwukG9LWUsKH6W2cRxUxHGbVY7XNe4bEzBnvxG1ELAgrwWjOzGBQRFAC6e+9PGSdsukV1IDAcFOuhy1p6mH4FadgDlXZ+c7MwQsyP06mIAJ5AlQfZBT/i6PKlbUT6BR+ZDPqVtNkaOzjG4uAuY8Fz7fnAhYkPtdMAETyBNAYG8ZxY9Oz/yRwklUx6KoBqWL82czm2Q5AuZcjpevnkLAgtyvhgmYQFECa0s6O04HxOTuo22Lkit3nTmX4zX6qy3IR/8KGIAJFCJwuzhEiMMmOD8gf359oU580UwC5jwTkS/IE7Ag9zthAiYwjQCm363isJ/nSTpG0r4dPFug7ytozn1fwZbHb0He8gL48SbQEwLLS9pHEmZfTvK7oCfj7tswzblvK9aB8VqQd2ARPAQT6AmBW0s6NwrDcKYzpwW61U/AnOtnOugeLcgHvbyenAnUTuDAKBbzIUnb1d67O0wEzNnvQmECFuSFUflCExgNgcdLWlfSYRNSzHaSdGikoT1a0vWjoVL/RM25fqaj7NGCfJTL7kmbwFQCt4jqbQ+KNLNdc1cSsX6IpPMkYV7/p1lWImDOlbD5pkkELMj9XpiACWQJ3CzKs1KC9cWSTs7h+YCkHSTtJ2l3o6tMwJwro/ONeQIW5H4nTMAE8gQ49Ww5SUfm/kBFNyq7kUOOWfhKo5uLgDnPhc83JwIW5H4XTMAEJm3wt5G0pqRTJV0oaaU48WxZSdtK+pmxzU2A319znhujO7Ag9ztgAiYwjQBa+XpxcMpfJJ0h6buS/m1ktRIw51pxjq8zC/LxrblnbAImYAImMCACFuQDWkxPxQRMwARMYHwELMjHt+aesQmYgAmYwIAIWJAPaDE9FRMwARMwgfERsCAf35p7xiZgAiZgAgMiYEE+oMX0VEzABEzABMZHwIJ8fGvuGZuACZiACQyIgAX5gBbTUzEBEzABExgfAQvy8a25Z2wCJmACJjAgAhbkA1pMT8UETMAETGB8BCzIx7fmnrEJmIAJmMCACFiQD2gxPRUTMAETMIHxEbAgH9+ae8YmYAImYAIDImBBPqDF9FRMwARMwATGR8CCfHxr7hmbgAmYgAkMiIAF+YAW01MxARMwARMYHwEL8vGtuWdsAiZgAiYwIAIW5ANaTE/FBEzABExgfAQsyMe35p6xCZiACZjAgAhYkA9oMT0VEzABEzCB8RGwIB/fmnvGJmACJmACAyJgQT6gxfRUTMAETMAExkfAgrz/a76MpJtJ+nv/p+IZmIAJmIAJlCVgQV6WWHeuv7WkPSTdIYZ0U0l7S/pNd4bokZiACZiACSyaQFuCHKHzQklPlLRiCKNLJB0o6fxFT7rh/pnr8yWtLunmkm4j6S6SjpD0pSljebCkF0n6i6T/SLqdpA9J+lHm+q0k/U3Sx+Oz+0t6haSdGp6fH2cCJmACJtAigTYEOYLtjSGwPxOCallJ+0jaWdKukj5QgsnTJL1H0uMk/anEfU1cCt9XSfq6pG9nHrhxCOA9Jb09NxDmsa8krvld/I3NzimSdpN0TnyGoGdjcHT8/0MlbSfp5U1MzM8wARMwARPoBoE2BPlTJa0i6cgcgltIOkPSAyU9RtJFBRGhqT5c0qMlXV/wnqYuQwv/hqTjQwj/Mx58qxDs95SE9v3z+Hx5SedKepOkk3ODRKvnc9hcI4nNzyslPUjSvyT9MTZDSfg3NUc/xwRMwARMoEUCbQhyBC+CHP/uebm5v1rSAZL2l/S6AlwQZvSBlrpjgeubvgShy9gul/SQELaMAU2azx8haR1JZ8XAnivpmDDD/yo32HuFaX0TSVgyUmMN+ffvpifn55mACZiACbRPoA1B/mlJG0g6XNL2OQQbhQkZbRSBNavdR9IPw9/+iVkXt/B3BPaWkhDKp2eev0K4Fu4UFohfxt+OlfTY0NL/mhvvbSX9IPrBhO5mAiZgAiZgAv/V5Jpua4Uv92BJF+ceTgDXUaGV8t+TGoFiq8Ufkj9589B6ScH6bvjds/eSnsXm4b6Sfi/puNBgCSTDLJ0aPDaVtKqkT2WCy9aU9GRJmP/xdROkxr1V29qSzg7fPn5v+mKMaOaY12F0Xa5zzPHfl/RbSY+3Bl4Vve8zARMwgWERaEOQTyPIWE4MQYqJmeCuSQ0hiwCnvUzS7SNgDNMyQvrzOSF779D+sQDQP4FjBIo9W9JXJO2VeciGkn4dQXMI6ydJelYIUALWEORfiEC191Z8FYhAxzT+4xg/kee0JKjxdSPokz89PSb9HaFPYNu1FZ/v20zABEzABAZEoEuC/H7h7z4zzOqzAteSf5xgsl2WEPpflfR6SR/LXJM0fzNc3j0AABDXSURBVFLgCESjoRET8X2QpLtL+klsCvgs669+W2jnZbRiTOw8Ez/388LiQGR6Vlgj4DGdXzFFkCe/Otfhb7cgH9AX0VMxARMwgaoEuiLIEaKYu4nyXk/SlQUmlPzjL5iivVPxDF87GjuadVZo4n//SER8/yyehaZP5DsCn5S2L4Y5/rO5sTBOgvXKCPJsF5jOSbVD636JpAvij3eUdKEk/OWTNHIL8gIvhS8xARMwgbER6Iogx0+8haT1QyMtsg74xYmApxDKZRNuWDfM4AjLfKobeeoI7WzKGsFkNHLR0brZIOAbpyhLalgBviXpm3MWXqEqG2lm+PsJbqMYDoVi0MjxgS9lWmcs1siLvCG+xgRMwARGQKALghy/NFHYW0u6ugRzhDi+YlK88v5kujlBElHw5Gnjjy4qjClY87Xwt1OUJdseIOl7kjaTdGqJsU66lCp2FIthHsz/lhGox7XkxedrpycfOZ+TtpYPhptzOL7dBEzABEygjwTaFuTkUFPoZPcoN5oYUj98KaFO0Bn54whcypLmG3//TkR2PzIn9Ah+w4TNxoHgt3y7a0Sr41fPV5h7rST+IdCvKrDgmN+xDBwWJvPsLZRSPTTS0LAM/COC71YOjTsFwaV70NiJWsd3T5/zRM0XGLovMQETMAET6AOBNgU55mHM45QpzQa2Yb4meA2NdVojjYzKbwSOkSZGQ9CtESbrpL0isPNaNSZzTO1URMM/zmaCVLBUUOXpkav9sIz/mv7xuZMeRr1zcsPx63Mv1egmtZSqxnMoIUvp2Wwj4v6Q2JBgXseq8E5JLw13ASb2bLtbCPF3BbM+vF9DHyPWoGfUNMls9kRNXbobEzCBMRBoS5ATvU2KGYIMTTTbENIEp3GoyLSGcCZYDf84VdNo+NiJeP9FCF182ZjB8ZGnxnw/GkIcTZ0ccuq7M47UEKYEw+EfzxZl4f+xApCPToobgXn8m2ZiR9ATUY9p/8UTSq6i7e8gab+wSPB8Ng+Mmw1CvuodnxGAh/aOZu7WPgHSF3nfUondeUZkQT4PPd9rAiMm0IYgv7Ok0yRR1SxbjCUtA+lV+KBJG5vW0MSJ/EZIYoJG+D8qIt/TPZSAZUPwzIy2jQUAvzQBbESmYyLH1J5Knib/OGZ9/OvZRiAe/mw0bP6ORo1mT93zaQ23wXITgu2YO6e8MXbM7ylKn+fzDPok7S2Zz1mnD4YVAH+6y7G2/6XF+sPGcaUO1vhvn45HYAIm0BiBNgQ5ZUjJ357WEO5Ubrt0iWuIMD8phB6m+KRpZzcGRIZjnscUTooXAWIUeSFIDG3/LREdTj53CixLZVDRjvKR7vjt2YBQBx4zNz/iszRjxrVNaPdo7pj6+eHnxDPGvW2Y97NTxUWAto41gaIz9MHhKFgfcDlko+gbe1H8oP8hQL0B3qUiZwIYnwmYgAksjEAbgryuyWC6xrSNNktFt2kNwYlwRKAnQY+QRxPns7xpnxPJKAAzyVqA35vCNT/NBefNmhNaOfnxxAUgiPGrU0p2mmbNuhC5zklxjAPrBNe7dYMAMRi8I2wOUx2CbozMozABExgdgT4L8tEtlifcGQJYUnD/4LaZ1HCR4FZho0khHzaS1AzAEoRVyM0ETMAEaiNgQV4bSnc0IgKkNu6dyZjITp3vFHEY1ObngJ3UCND8eGQc4FpxMwETMIFaCFiQ14LRnYyIANkOHJlL5sUk1whaONkK1PCnYmEqVoQ5HsGO64YgzToi3UeE3VM1AROYRsCC3O+GCZQjQFYBfvFpWjW55edEWiQxEZxmR0u18vGrk0pITQI3EzABE5ibgAX53AjdwYgIcAAPmjRaN6fUTWoIbAoGEQx3euaCFSLlkNTDB06o9DcijJ6qCZhAnQQsyOuk6b6GTgDfNwfaEMhWtnEfFQSp8ofJ3SV2yxL09SZgAhMJWJD7xWiaAGmDpATO8+4hBDnudVKK4CLnQ7rijjOKFU16PkWOKDrE4T0UEsrX0V/kmN23CZjAwAnM82M6cDSe3oIIUBmPYDEEetWGIKfEL8e+NtXI6X9f1PMv8kxM7FtFUByVCI+RRPGhSSf1FenP15iACZjATI3ctZ79khQlMMZ3hdQxUsoOLgopc93yUVIY8zq1/6k06GYCJmACtRDIauRj/HGuBeIIOxnSu/IESanG/rSl5GhbzOKrZKLQyy471QTPjcIwnHZ3SdkOfL0JmIAJTCJg07rfizET4FCdk+OUO9LC8kfHJjZvDiHOgTXzNGr/EzBHCtu8fc0zDt9rAiYwIAIW5ANaTE+lFAF83ifGmfZrSXpKlFzNR5OjrV8m6TkF691zmt26kg6bkGK2k6RDIw2N42ivLzViX2wCJmACEwhYkPu1aJoAOdRUPiOSu2r7syRM4lV9zatGlTWC0L4cEfSfixPt3pEbFMfZviGOyZ01Xg7VoXobAX2kme2au4GI9UPirHnM6w58m0XUfzcBE5hJwIJ8JiJfUDMBNNx7zBm1TtoZBVfmOZf9PnGKXZoehVqoob5FBLWlzz8v6QRJHy7AgUh8NimUYH1xmO2zt3E87Q6S9pO0e4H+fIkJmIAJzCRgQT4T0cIuoEoYZ4xzFvpFcbb1wh7mjgsRwCz+kTie9CpJCHsC1Mh7v7ZQDzcUi+HY2vx59mwUzo8ccp7D8btuJmACJjA3AQvyuRGW7gCtDa2MQzTQAB8X+cbvDr+qK36VRlrrDZjRWZMNQnMmHzxvIl/qgXyntpG0pqRTJV0YGwFqsy8riSNQfYZ5rUvmzkxg3AQsyJtf/60lXSrpjMyjN5F0Uphj0Qjd2iOA6f8LsT5EmOPLJvWsbEMrX08SB6f8Jfr77pzugLJj8PUmYAIjIGBB3uwio41/StK3JL1T0j/i8eQYo51TupPTs9LnzY7OT0sE7hJm8B9KepqxmIAJmECXCViQN7s6RDWjlXGW9X0l/Sbz+K/GqVoESv2+2WH9z9OWiWA0/PdjbeSY49fGUuJmAiZgAp0lYEHe/NIgqG8b0c3p6fjLSVsiHemRLeYXYxnYQ9IdYmCYmffObTiaJ+YnmoAJmIAJTCVQRpATYX2ApBfNUabSSzGZAMVBzpL0+mA8ixMCluhozsUmGOs2UfrzCElfmnIzGwjWDn8tAXXkcVNhjBO9UuOQD8z71BWnseavkEQhEzcTMAETMIEOEpglyMmFvV8ICapVYRqm2EXbpt+qKPF3UqiDqOQ/Ve2k5vswY58SZULhPavaF2tGEBYHeKDFp7ZxCOA9JREhnW3Ml5O3uOZ38YcV47mcjX1OfIagZ2NwdPz/Q6OU6MtrnrO7MwETMAETqInALEH+sNC+fxFCggjePgtyNNCHS+pSeUwEKYIWIX5NgXVFC6foyPGSuDdVB0vm+XtGQZKfR1+cvEUu9JsmFChBq+dzAux4NulRr4w1pujKH+PUriT8CwzPl5iACZiACTRJYJYgz46FM6T7LMgRUueF9rljk5CXeNZmUWr0tVEYpsiwELpo0JdHahPCloYmzecc/rFOmOr5nHO7OQubDQDV0LKNoDtM66S/fSbzB94L/s1TOa3IXHyNCZiACZjAnATGJMip0kU60QslsSlpu1Hdi3+YvNF+aQjh788wryOwtwyhfHpmEitEyhSR1tQz/2X87djYgOEj/2tu0gTd/UAS/fg0rrbfCD/fBEzABCoQGLogJx94teCS/MSbhzZLahWpYPlKauR6U9WL9DBiAY4LzZTrksClS9htKokDOMgNT0FjVPR6csQT4MMm+Cz/DIqEcOgHJ2FltV7M2u+reJjG2pLOjhgATO48k7kQRId5nRO+rsu9I5jj2ThwfCebCmvgFb5EvsUETMAE2iQwdEGOkEWA0zh5ivrmBIIhsBDSHIiRFbL3lnR4/OOISwLCCAB7tqSvSNors1gbSvp1BM0hrMk7flYIRgLRCAykQhgR4O/N3MeY8NWfmVt4hO0tY5xl3wki0DGNU4GMeRJ5TkuCGvM7gj5/2lb6OwwIbCtaT7zs+Hy9CZiACZjAgggMXZAnbMk/TpDYLlNYImApykIK2Mcy15CSdVSY5Akwo6HpEsl9kKS7S/pJbAr4LOuHflto50nbJUIdoY82PqkReJaPOJ+29JjYGRt+bo7jxA+OmT4rrBHwmM6vmCLIk1+d67ASWJAv6Ivmbk3ABExgUQTGIsiTf/wFkXKV54mAPTk0djTrrDAkEIz650Trp8MuEPpEviPwSWn7YpjjP5vrGLP8Kg2YrdHm9wlh/ZLMOd13jEM78JdP0sgtyBf1zXK/JmACJtAQgaYFOdojEeNlnptFgc85FSspgwi/OOZsCpxcNuFGcuQxgyME88dPcoY0QjubskaQGI1cdLRuNgj4xim2khpWAGqqf7OhgipUZSPNjLgAsgsuiUIxaOT4wJcyrTNma+Rl3ihfawImYAIdIVBGoNaRfkaO885zCHIOFsF3XbYhxPEBk7qV9xPT1wmSNor86+xJV7OEMRXWvhb+doqtZNsDJH1PEilmHGfZRDswisUwX6LQ8bkT0Ecjfz5fOz35yPmciPl8MFwTY/YzTMAETMAE5iDQtCCfY6iVbyXojPxxBC7lRvONv7NBIACOOudZYUbwG+dJc/TopA3EXSNaHb86mnu2kRvOPwT6VZVH/7834m/HgnBYJsUsXUUpVSLhzw8LAqeoEaS3cmjcKQguXU9pV6LW8fHTp89Cr3Gh3JUJmIAJNEFgDIKcNLKLIiCMNDEaAmyNMEUnrRSBndeqMZljak/+cQqtkOKV0rSeHjnYVMC7ILNg+NxJ+yIljZxvguO4N3sGeZX1ZdOBe4HxUGp211wnRKwfEhsXzOtYHzgu9aXhVsDEnm13CyH+LkmUdnUzARMwARPoGYExCHKEM8Fq+MephkbbItK/KD2L0MWXjRkcH3lqsPloCE00dXLIcQsgKFNDSBIMh388W2yF/8cKQD46KW5UVePfvCZ2NgRE3lPchZKuBOhlG1aBHSTtJ2n3+AObDObHRoIxZRufEaiH/x/N3M0ETMAETKBnBMoIcvKUCZjCVHxlj+ZJahYR3Qg/TMto6I+KQi9pGhzdSbT6MzPaNgFyHE5CABuR6cwbU3sqZZr841eHfz2LZP0IrkNz5u9oymj2RWqpz0JLffTlJgTlUdENkzpzxPye1ohx4jPn2aTHJfM5a//BsBbgT3cxmFnk/XcTMAET6CCBWYIcnzKV0RASBEuhEZKCdXH88L8lF6ndwSn+9+zvk0KYEbyWNO1slTYivgkUwxSOiZzAL/K98ZdzNCjzZBNDnnYKGEvlTSkSk4905zzv0yTtLwnzNcVf6tJ4Gf82YQVAw8clsFLknzO/bTNpcmk9cCWgrWN1oDgNfVBFDisFefXZaPsurqHHZAImYAImMIXALEE+FHBsQDBto6UudQQrAhGhh0BPgh4hjybOZwSPZRtR+BSAyW4K0t/xZ3ME7E8zldbq5IlWvl4EsSGI8b8ToT5Ns2at2Yw9NcZL8ZsU0V7nuNyXCZiACZhAgwTGIsgbROpHmYAJmIAJmEBzBCzIm2PtJ5mACZiACZhA7QQsyGtH6g5NwARMwARMoDkCFuTNsfaTTMAETMAETKB2AhbktSN1hyZgAiZgAibQHAEL8uZY+0kmYAImYAImUDsBC/LakbpDEzABEzABE2iOgAV5c6z9JBMwARMwAROonYAFee1I3aEJmIAJmIAJNEfAgrw51n6SCZiACZiACdROwIK8dqTu0ARMwARMwASaI/B/TT6NSDDiR84AAAAASUVORK5CYII=)
Now according to options,
![](data:image/png;base64,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)
Out of the given alternatives, only tan 60° = ![](data:image/png;base64,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)
Hence, (C) is correct
Question 6.If
and ![](data:image/png;base64,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)
find A and B
Answer:Now, we know that
![](data:image/png;base64,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)
So, from the question we can tell,
tan (A + B) = ![](data:image/png;base64,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)
tan (A + B) = tan 60o
A + B = 60° .......eq (i)
And
tan (A – B) = ![](data:image/png;base64,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)
tan (A - B) = tan 30°
A - B = 30 ...........eq(ii)
On adding both equations, we obtain
2 A = 90°
⇒ A = 45
From equation (i), we obtain
45 + B = 60
B = 15o
Therefore, ∠A = 45° and ∠B = 15°
Question 7.State whether the following are true or false. Justify your answer
(i) Sin (A + B) = sin A + sin B
(ii) The value of sin θ increases as θ increases
(iii) The value of cos θ increases as θ increases.
(iv) Sin θ = cos θ for all values of θ.
(v) Cot A is not defined for A = 0°
Answer:(i) sin (A + B) = sin A + sin B
Let A = 30° and B = 60°
sin (A + B) = sin (30° + 60°) = sin 90°
= 1
sin A + sin B = sin 30° + sin 60°
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Clearly, sin (A + B) ≠sin A + sin B
Hence, the given statement is false
(ii) The value of sin θ increases as θ increases in the interval of 0° < θ < 90° as sin 0° = 0
sin 30o = ![](data:image/png;base64,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)
sin 45o =
= 0.707
sin 60o =
= 0.886
sin 90° = 1
Clearly the value increases.
Hence, the given statement is true
(iii) cos 0° = 1
cos 30o = ![](data:image/png;base64,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)
cos 45o = ![](data:image/png;base64,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)
cos 60o = ![](data:image/png;base64,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)
cos 90° = 0
It can be observed that the value of cos θ does not increase in the interval of 0° < θ < 90°
Hence, the given statement is false
(iv) sin θ = cos θ for all values of θ.
This is true when θ = 45°
As,
sin 45o = ![](data:image/png;base64,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)
cos 45o = ![](data:image/png;base64,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)
It is not true for all other values of θ
As sin 30o =
and cos 30o = ![](data:image/png;base64,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)
Hence, the given statement is false
(v) cot A is not defined for A = 0°
cot A = ![](data:image/png;base64,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)
cot 0o = ![](data:image/png;base64,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)
=
=undefined
Hence, the given statement is true
Evaluate the following:
(i)
(ii)
(iii)
(iv)
(v)
Answer:
Given is the table of Trigonometrical ratios for different values. Use the values from table for solving the questions.
(i) sin60° cos30° + sin30° cos 60°
= 1
(ii) 2 tan245° + cos230° - sin260°
= 2 (1)2 + (√3/2)2 - (√3/2)2
= 2 + 3/4 - 3/4
= 2
(iii)
As the denominator has an irrational number, we need to rationalize the fraction
(iv)
(v)
Question 2.
Choose the correct option and justify your choice:
A. sin 60°
B. cos 60°
C. tan 60°
D. sin 30°
Answer:
(i) We know that,
Putting values in given equation,
in options we have,
sin 60° = √3/2
cos 60° = ½
tan 60° = √3
sin 30° = ½
Only (A) is correct.
Question 3.
Choose the correct option and justify your choice:
A. tan 90°
B. 1
C. sin 45°
D. 0
Answer:
=
=
= 0
Hence, (D) is correct
Question 4.
Choose the correct option and justify your choice:
Sin 2A = 2 sin A is true when A =
A. 0°
B. 30°
C. 45°
D. 60°
Answer:
Out of the given alternatives, only A = 0° is correct
As
sin 2A = sin 0° = 0
2 sin A = 2sin 0° = 2(0) = 0
Hence, (A) is correct
Question 5.
Choose the correct option and justify your choice:
A. Cos 60°
B. sin 60°
C. tan 60°
D. sin 30°
Answer:
Now according to options,
Out of the given alternatives, only tan 60° =
Hence, (C) is correct
Question 6.
If and
find A and B
Answer:
Now, we know that
So, from the question we can tell,
tan (A + B) =
tan (A + B) = tan 60o
A + B = 60° .......eq (i)
And
tan (A – B) =
tan (A - B) = tan 30°
A - B = 30 ...........eq(ii)
On adding both equations, we obtain
2 A = 90°
⇒ A = 45
From equation (i), we obtain
45 + B = 60
B = 15o
Therefore, ∠A = 45° and ∠B = 15°
Question 7.
State whether the following are true or false. Justify your answer
(i) Sin (A + B) = sin A + sin B
(ii) The value of sin θ increases as θ increases
(iii) The value of cos θ increases as θ increases.
(iv) Sin θ = cos θ for all values of θ.
(v) Cot A is not defined for A = 0°
Answer:
(i) sin (A + B) = sin A + sin B
Let A = 30° and B = 60°
sin (A + B) = sin (30° + 60°) = sin 90°
= 1
sin A + sin B = sin 30° + sin 60°
=
=
Clearly, sin (A + B) ≠sin A + sin B
Hence, the given statement is false
(ii) The value of sin θ increases as θ increases in the interval of 0° < θ < 90° as sin 0° = 0
sin 30o =
sin 45o = = 0.707
sin 60o = = 0.886
sin 90° = 1
Clearly the value increases.Hence, the given statement is true
(iii) cos 0° = 1
cos 30o =
cos 45o =
cos 60o =
cos 90° = 0
It can be observed that the value of cos θ does not increase in the interval of 0° < θ < 90°
Hence, the given statement is false
(iv) sin θ = cos θ for all values of θ.
This is true when θ = 45°
As,
sin 45o =
cos 45o =
It is not true for all other values of θ
As sin 30o = and cos 30o =
Hence, the given statement is false
(v) cot A is not defined for A = 0°
cot A =
cot 0o =
= =undefined
Hence, the given statement is true
Exercise 8.3
Question 1.Evaluate:
(i) ![](data:image/png;base64,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)
(ii) ![](data:image/png;base64,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)
(iii) Cos 48° – sin 42°
(iv) Cosec 31° – sec 59°
Answer:
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3hSYB1R7ruzoubhNrLYyNxUPp5YeAO4WV8Kz7Uy3wMIJnoeZa2aP4luUVNrAy5tSNT4t3mcUnHcK6PpAwBPxnelh6ZoaOkpbbkNWYB61ZISgxOF0S8qI/bcnyo7YuZCa9nhQ00jUdNUu62LmqJxZ25bg8O97sY6fmBd3RIql4Uut7WprgITAeXpmCn0blwNKp1m6GBAukzqxspmprlM7X9xHUfENcrNr48dvWht5SkTAF3s1ar3s9d0EzW/YKQyvV6uGa6Hh3CsZ+7MZjccE6/3HmQC9rNyOya+sQq8z+vz4eLMSqAS4R9TXtSD3H+FMTrdiXgJdGnMwMuKDHTQ+wjKTN54qFn6ca4DJGuinmL569r++8KTM2kNt1qkjKE0xiuGR5P3XE9JImnuNpm9949g6TKMcML05110+PRZRfgZUOHWQBKdqaw1S1qUjWr9IJIV+tpbFt7GnAZQOI0xClNXA3hxMSQV49FElJYlaS6m4Jh1HsB0/kSnGH6svM/D1M9zm+GRy3Z9DVr7D4WyQ49v9K0R/uvh2BfJCnDPElULzRJ6v+RGsP23XSNfgzJm241SbkjvQK4VOxMxqruUG+riufKYJYhKcNE3f4uSXntGDueRXvunhp73c4SnpREpUC4TU2N0DBKcrKqfp7+YihlvZjesRtPX5PM9KTMmnnPZed/HqaSpwRjRm5euC1x6m3ZN8/XFtUS1cneEiUKhrWO2eM/WRDu2acx7Ko7NrOH1t4NTTJpn6WwdCxbHMP2rV073gxMx+rnKPfpAm+mxPd79IJ0221qAdYeGb+2QlIK+wrl7q7ddnTgpuH5XXQUlNq5iR6ItS3vjAzmvJ5Z/Kj2YzGliYW+pmd7/Sh8NeO27PyPQVLeQ+/tWvE+n7KA43KzVINyYUtaeoK+RWA7Y48UUTQpvWk9r7Hf1ZPslQ6GkpTazyyPcohljWX7elKOrc87HdKvjV1TA1/XlZgmdnfVFdSIzLi4c5fq8v32pCzqU4f6QQ8yhq1fD49D4fXvG0Nv729sJu+rMQ+L3PSSyp9HUlZluyEpVksMpa5o0fzPG/ky4d686y3iNLFy3aixsk/qnxK0nlKtcXofw0E9Ld+CUOvc9jaW7U8y3NMIdMFrEdoJP3hoG4Z/iuG2/SQptRcXlV5AXyt1M2pefUY9xIgV5/VKDC+HNt83E7du8eIq95M8LHA8VGh73QXrvdSaJGb1BsM9hWlLQ/qa2VYxchMyrFp2/uf1ueBvRthM66ymR/DLnnfItDFfYTFsLJuQQruvtvgenmFf3Qpx+7x7rQLmBM8dy/YlfjVl8Z2UcC5JmdbWoLsiq+6uKW5DrP0kKQVD0+wKq90MZLE5SVUdwLBPcinvea1jk4rQemgSwNAmcVjYuG4dz41jnvQSy/tqpU8a3+1D6/E51qqpDZnlKy/llnOdT70ntTszbavM/zwMSgmC9XD2ta/p5Un6PluPqTRDNws5Ffz1GEozE+nnevNdDdLP3hohq+PZ1jam7YuzIbQbvTbSdKvDPY1Ul1l3uxa8PceQ4XFVuFdcco3/U50RWj/lDm3VtxpD3Xwj3peS3b0t9FylCaxCqxrZXedc6GRq0Hpb21h1rjdlmGYhn0mOumLYDcY6olKHpudnHZXJDz2Usvk4p5K9eoSZQgt3V5n/RfNm6YnkofDdF277ufVZej4Pqm7mV4kYskmstZdYbNCx+j5gPY6nxOah7jZGWcuise3H8bFt30JaM6bOQ7cEZD/GN/eZXZIyvW2s6kI3LDEEsCbK3UvxzxDC2iMN+qjAz8Nt9Pt79DRk5XJMV9I/C/oEQ4HWr+4QcIsK1RlcKIua4cNTwxvQkzFMMDNhxqX2pvQMTGeX2hoXq0Qoid4D+PaiB03ouN6i5RXqUhbLGgJZPyWu3W8ccA4lAz3LN8YYTSiYdJAgCsk5b4vmf1mIJD8zdL5I3H3txXtoX5KmGqcygkkawzlrtaxz6/vCQs/R07fQ0w1T25WwfIaefvOvdywLXnXepmzfrLcbvZnwPslgQFc3d0lNUhqOf062mofCuYtcEbpb5bu5HuWdV0FAspKc/EoaCWreV9OUc72/c9rNgo05/+UFY18knqUdGhYaspqFLN7folemtFczfHrphrN66iXztwpuu3xuecFYbdOC4Obb0LRq8wPLDu47ApYP+DqOYd/YZQH7PrgJd8Dkg3KM3u4kviUkSWrC1tZ419XOLA5VJui+edB417e2e+VL73zTwNB5Ei1JahLTNNlOqkFKUnpVviqTbX8R8BtJ/Nv6rw/eX5jz6VNDwNoeSxz8krv8BZ/9mz3n4Y678kMM+wdzPnmqCJw0srvWPm3TGwBTmQ8zt74qZjZ9clnQDPemYmbZz0RgRxFIktrRic9hJwJTQSBJaiozlf1MBHYUgSSpHZ34HHYiMBUEkqSmMlPZz0RgRxFIktrRic9hJwJTQSBJaiozlf1MBHYUgSSpHZ34HHYiMBUEkqSmMlPZz0RgRxFIktrRic9hJwJTQSBJaiozlf1MBHYUgSSpHZ34HHYiMBUEkqSmMlPZz0RgRxFIktrRic9hJwJTQSBJaiozlf1MBHYUgSSpHZ34HHYiMBUEkqSmMlPZz0RgRxFIktrRic9hJwJTQSBJaiozlf1MBHYUgSSpHZ34HHYiMBUEkqSmMlPZz0RgRxFIktrRic9hJwJTQSBJaiozlf1MBHYUgV0hKX9e+nD545RNWfmpgOsCd97D3+Lzp9+1hT83hcQ4nZll4/7m3s2B+0/xN/eEZldIykk6N3C1cewh77ImAmcDbgfcEPj1mvda5vJDAncBjhwnu6DvA/xomYsncs48Gz9r4O2vSO8F3qNCtgskdWzgE8DngAuOil7ebAgCJwCeD1wB+GHPDU4P3Az4JfA34PDAo4CvzXjYaYBrAL+J40cAngZ8pTr/OsAfgJfGZ6cAbhHPGTKG1q5ZxsbF+3LA9YC/tjaAef2ZRVKXAD6+BTuN43skcBPgC4A7+KQmqCFjGsMmDga8CngG8LKesV0VuC9w8YqUTgu8EPDYZzvXnAt4SCy+n8axYwCvBG4LfDA+k8QOCjw7/u099eIkqqm3ZW1c7/G5wEeD9Ccz7lkkpU7gbvfdyYykv6PnBM4E3KYyzt9NfEz71f0xbMJw+5bAAcBfOgM5JfAB4E7AkzvHHg6cAbhItckcOhbc3YKU6kuuAtwdODvwe0At6taAOtg/Qpt8IPCz/QJzxOeuYuOnBl4PnAf4zoh92Oit+kjKz94AGL9OmaQOEWLhvYH3ACeJv23SITZqHNXNx7AJvaj3AY+vPJq6/xKTNme49+nOwPTiXgecA/hQHDN0eQ5wcuD7nfOPD3wJuGJcVw47Dv8kqm1oq9q4YxdHpQ83g0m0PpI6M/AuwLh9yiRl7P3FMOq3AxcATtbRKiYxSQ10cgybcMd389Ob6ZKKns5HgqCO22N3Cr8fDrHbTcf2PMB7Grp1vWN1LEPDN0dY1wCEG+nCEBs39L1nRBiTiCpqkjoMcH7gCcBxgMsDPwloFTi/0dlZ1Q00qL8DxwqNQYau2xGBS8bxwwIPC/fbex8F8LPXAp8feQqPCdwAeADwT+DFwJUjw/f+kZ/V0u0UjTVcdZk/Ab+NxdznPYr/tYE/AgcJzUbP5BfVgFaxiUU4PDTCr/P1eDJm3z4DnDhsqrs5Ko57XJLTq7K/emXaj+F8t6Sg3O/HwHm3yHOqMR5q4yeK9WYSaRJroSapMwLqAhLV9YFbVQar6GyGzKYAd4cwmCJkHi/+rSsvyZVmyvfSkX0RFHe9CwEvisyOOoOG58J60yIrX+G4esTTq+yR2SHHY4igcDtGEwfJ3P8ObYYd3xtpEakzPCnqjnTpJWc3CbWXx0bioPTzwjGHisffig/1Mh8DSCZ6nrZlbWLR+MXIkNswzlR5t3lc0jGc6/OkDAE/Gd6W3pOho6T1q7jGLGDdCkmJwemCiBf1cWrHh9q42JgUe1bMdfPj7gv3NNynzDAWBySRaWx6J9eKxeDnEoDZA3e2L3dG7qLQ9bY2xUVgOrg0hTyNznM0qnWboYEhxTOrGymamuUztf3EdR8Q1ytCvjx29aG3lKRMDXezVqvez93RTNb9gpDK9ZcNUfnRIRz7uRvDa2Kz6M6TC1rPVi+59ooX2cSi/lpI6xgVwCXCvvbg0EmcPzNQdbsS8JLok6GnC8376SFKbF2SMpMnHnqWbox6i9vU1rVx5RyxM2PafBtCUlawfiw8HyuGC7GcEPg6cM3IDNaD1+V+d4QXElnd9HgkNoHvZnxWBVCyM4WtbmG4U5pZpRdEutos1bY164IuA0ichjiliashnJi4qeixSEIKrnq03U3BMOq9gOl8Ca4cX5ek9Di/GR61ZNPXil1ZGa3nV5o2av/1HCQmScowTxLVC901khrDxt1cjXIMvZtvQ0jKQblTqUVpxP7/kcLDemdkaJ7aGXkhKVPPuv1dkvL4GDueRXvunpJo3c4SnpREpXC4TU3dSM9WcrKqfl7mylDK0N2Q182kr0lmelJ11mxdkpI8JZhF4bbEqbdl3zxf+1RLVCd7S5QoGNY6Zo+rmfaRVAn3HN8YduV9zBhabze0AFqbLMWk69jfGDZujZoSTR926/RtI9cOJSmzMbqKipjfDtda8bKULuwHSR0thHJ31247OnDTCDkvuhEk9++meiDWvLhBmMGc1yx+VPuxmNLEQl/Ts1WTtPDVjJttr0jKZ5mEUUZwE1QWcFxuhGpQLnJJS0+waKTqZrXX7D0KSfm5ntcY7+pJ8MoFQ0lKHWiWF7ms9Yxl43pSjmerSErNQ4FVw9FTsaLXHVuiKpW+ZbFY67IfJGVRnzrUD3pm3NcGDEX1OBReHce2NDN5Xw0xdJH7XlL580jKqmyzfnW9Uh9J1TaxCMtlwr1597CI08SK8oL9kyjeAWhzekq1xul9DAf1tHw1Rq1zW9pYNr6V4Z4vZ5ohU4BUeJacNI46VdwlKRdE2Yk3He6pvbio9AL6WqmbUfPqM+ohRqw4r1ciaQ9tvm8mNt3ixVXup1drgeOhQtvrLljvpdYkMatDGO4pTFsa0tf0hsXItL/vz9n6SKq2iUX9Lfg/YsErGXoKPrP76pIJF19hMWwsm5BCu/2ynq+UypR+FOL2efda1LmJHB/LxiV49WFxnKxw7i7qbmXMWkrn/ydeVdDYdbPVCLr1J7rdurTFk/Kax4UBbJKkFBJNsyusdt3+Yn8HD53KsE9yKd7fOvapCK2HJiZDm8RhYeO6FdA3jvIDvcTyvlrpk0Z5+9B6fI61ampDZvnKS7nlXEsWDKvU7uqK5Hk2scy7kKUEwXo4+9rX3NQkfZ+tx1SaoZuFnAr+ehKlmYn0c3W4rgbpZ2+NkNXxTL2NaePi6Rp2Q9cWmm998bW7lTut9U1OtHqAeo4ZF43NGhwXuqT08xihn7ur+Y6coZ47mP/vf20XC71KzUSNoW6+I+g7Vu7evme1ShNwhVbrZe4650InWYPW29rGqnO9KTcWC/wu1anA1mMyRV/q0PT8nMO3RUlIyeBpC5K9OoWZwvorPebZxLLzZemJ5KHw3Rdu+7n1WXo+D6pu6le6GLJJrLWXaH8NW62a9n3AehyW0Lh5qLuNUday7Bg3cd7YNm7BrJlR8e6Wemyi/2vfc9a7e+68CpTW15jVMBtU6mbUF/SQFC9LzctJ4011szO65r61/upww2VrQ8Gjhoupm2lBnyAp0PrVHU6Empc6gwtlUTN8kAz1BjRGwwQzFmZfam9Kz0ByLbU1LlaJ8FPAPUL0X/SsqRzXW7S8Ql3KYllDoKIbdb9xwOyYZKBn+cYYoAkFkw4SRPd1ieKNzbKJZTCS/MzQWWfX97qVG4m2ozduJbS1VW58VsZb5+ZG1G2eYwGrhZ7apP2UsHyGIvckXvuYAd6mbNzsthu6Ge8+aWCZudzTc+ZlKhQfZV2/x8fXK/oMxAyBxmPIUnYsjc2woltgt6cD2+GHSVaSk2GYxLjD+08AAA2bSURBVD8vHCvnCpeJhUVZsEU2MQ/28oKxLxLP0g71yA1ZzUIW72/RK1PasF69Xrp2p6deMn87bAa9Qy8vGKthWvg7iTY0nTqJwWUnm0NAT8xXqgz7FhFic53fgg6ZZDAxolc7mW8DSZLaAsub0BDUzl4R9ULdNw8mNIxJdrV86Z1vFBgiT6YlSU1mqramo2qQFjXqVfmqTLa9QcBvHvFva74+eG9gy6fsKgLW/FjiYLlKnyC+q7hsatzifcfAO3+IYVMo5323DgEzwmZ3rX3apjcAWpsoM+uWEJk1n2S2M8O91kwq+5MIJAL/hkCSVBpEIpAINI1AklTT05OdSwQSgSSptIFEIBFoGoEkqaanJzuXCCQCSVJpA4lAItA0AklSTU9Pdi4RSASSpNIGEoFEoGkEkqSanp7sXCKQCCRJpQ0kAolA0wgkSTU9Pdm5RCARSJJKG0gEEoGmEUiSanp6snOJQCKQJJU2kAgkAk0jkCTV9PRk5xKBRCBJKm0gEUgEmkYgSarp6cnOJQKJQJJU2kAikAg0jUCSVNPTk51LBBKBJKm0gUQgEWgagSSppqcnO5cIJAJJUmkDiUAi0DQCSVJNT092LhFIBJKkhtmAP1l9uPxhy2HgbeCqUwHXBe68h7/h50/Gawd/3sB49vuWs+zb3/C7OXD/vfwNvySpYebgRJ0buNqwy/OqERE4G3A74IbAXvw67yGBuwBHjjG4oO8D/GjEMe33rebZ91kDb399ei/wJklqdXM4NvAJ4HPABVe/PK8YEYETAM8HrgD8sOe+pwduBvwS+BtweOBRwNdm9OE0wDWA38TxIwBPA75SnX8d4A/AS+OzUwC3iOeMOLR9u9Uy9i3elwOuB/x10z1NkloNYfF6JHAT4AuAu/jGJ2m1Lu7M2QcDXgU8A3hZz6ivCtwXuHhFSqcFXgh47LOda84FPCQW30/j2DGAVwK3BT4Yn0liBwWeHf/2nnpxEtXU27L2rff4XOCjQfobHXeS1GrwnhM4E3CbykB/t9ot8uyREDDUviVwAPCXzj1PCXwAuBPw5M6xhwNnAC5SbTCHjgV3tyCl+pKrAHcHzg78HlCLujWgDvaP0CUfCPxspHHt521Wse9TA68HzgN8Z5OdTpJaHt1DhGB4b+A9wEnib5u0iOXR2N8z9aLeBzy+8mjqHklMaiaGe5/udPUSwOuAcwAfimOGLs8BTg58v3P+8YEvAVeM68ph145/EtU2tFXt27GLo7KHm8HGWpLU8tAaf38xDPvtwAWAk3X0iuXvlmeug4A7/hvCm+mSip7OR4Kgjgt8t/Mghd8Ph9jthmN7HuA9Dd26nrE6lqHhmyOsW6ffLV87xL4Nfe8Z0cXGIopZJKVgaKeNyf8E/DYmss9rOApwbeCPwEEiXndX+kVnRnzWhYCjRVbgMCF26pF4fu2ynzR0g5+E2Kn+o2vZt2ut0tehRnJM4AbAA4B/Ai8GrhwZvvcPvWnD17U+Vw+N8Ot8PTZh9u0zwImBPpJSHPe4JKdXpc3qlR02Flu3pKDc78fAebfIc6rNb6h9nwj4fCSQNrYO+kjKGPNJUXOiO+eiPCJg3P3YEIzLAC8M3CF2mG/Fh3oXjwE0JD2O0ozrdb1fW32mnvCIWOySnP25KXD1IIEfhAZgRsYd0kyNWZrSVunrOpxg359eZZDsz61CZFW8HaMpRh4nam+G3k8S/94IC6nluRInw21tyVR5t3lc0jGc6yMpQ8BPhrel92ToKGn9Kq6p7ct7F5JyHZwuNuOh89PqdUPtW2w+Djwr1vtGxtclKZnRLMb9gpDKQy8bguKjQzT0c8XH14R39OVO75xMycjMijGr3paLWU9Kz6xuDw7XW5KS9MzUSD61luD1GpIZlJfHxav0dR3wDA8USZ9Z3UTh1CyfpPnEdW5eXasQ6djc2Yc2Scr0cDdztcr9Wp8ri2gdnwK4m2Ff06bUSZw7M1B1uxLwkrDLMwcJeT+jBImtS1Jm8lwTeuyGg9rpNrV17ftdgZ0Z0420LklZE3IZwAWje1uaGS1DMlO6hjruVpKQYpvE4y5TNxfaewFTuRLcscKwrhludn3upSPed4G5A/49SMr/1u3V8dxLxYfL9nUd4NxlHbPaRU2uZpZeEClrq5y3qVkn46Jtda70Nr8Z9UySTV+zMvpjkejQ+y9Ne3c+9RwcoyRlmOdGqge6ayQ1hn27sVrYaui9kVaTlBqR3ovkZDX1vKyFbrQ6kd6RxtzXJDM9KTMm3vMVgATjrmT86n/fVhXOqSEoTOtJ9VVyPy50CFPBkuOyfV0HOAv33EE1+LqdJTwpiUrxcJuankPLc+UGKsGYkZsXart56m1pn56vrasjqpW+JUoU9Ni1e4+rf/aRVAn3nOOxPCkzhtbaDU1caY+lmHQd2xvDvl2vx5uB3Tp9+7edpfzD3cd6h3dG5mreAyx80+uxkE5Bua+p4Vw/Ch7Ntpgl8Z0fRXZddps6gDVHxrSKku8OvUCvqa+ZqfFcd/tl+zoUKAV+hXJ32G47emhnZnwuOvQBDV/X8lwtS1LCqwd/rfDOrRLXtiVhpQMXuaTlhucbBLYz9sgRhaT0pPW8xnhXz01eqWAoSakDzfIilzWrsexbT8rx9BH8sn2Ze14Nkpm8r4YQtsh1K2nceSRlRa6EpFCpUZSaEgVwvSufoQGZbdFz87j6gSRkZnFeW6WvQ4GysE8dSvG+2yTJr4c3p/jaDU2HPrOF6+r6nxbnaplwbx6OFnG+KV5I1kYd7zsAN2k9JcmsboaDelq+GqNmui1tLPve03BPg7S47VCRiu1OlpOj1uSCNAY13JNULjlj1kzxOumSkC617nctPnvZwUPbMvxTlNcYTGnO8k7cBRU2V+nrEKNSg5Nc9Qb7WqmdsWyiz7CHPFNxXu/U8HJo850zPdJuAeMq93OxtjxXBXuzwmZZZzU9Bd/Z67625MvAJmD0yMoGpNDuqy2+h2fYV7eyIfq8e60CZMPnjmXfErzRjzjumXB+4yg/0Dso7yoVrO3Q7SPOV696WOgCZvnKC5nlXEsW9J7UbMyyaPiWNUhoXZFdt9fzDa38swShNqBZz1+lr6vYi2Ki5RaKq91MZLmP5KouYNgnuZR3vVZ5TvdckxF6aOtk99xALG5cpwq69bkqJQhuZtpAX9PTl/C1P7/CpTRDNws5TfroSZRmNtrP9ei7+qOfvTVkC2166m1M+xZPQ2U3c/lgI60bE+uh6AJb3KXIXVeRSjB6MbrKNnd866gUv92dCvl4Txe5MaqZQr/OQcPXXdbVtsalJh5DRkVx42y9ON1H9SZrYOp0sFlC76WuYFulr8uCJ+iKrWpld51zkROtUettbVvV+RTmyho8yUPhuy/U9nNr9PR8HlTNo1/pYsim6F5HCtqsdqi9+z5gbctPiY1D7bW7wS5rV62cN7Z9m+wyMyre3VKP0cbcJ9zpJZhWVzN6Ubi/1iRZrNl929wwTkPQo3hj9MpQTbFZ4ygkp+FbMiABucANR7z2/LFz1SKgn+vFWInujqcx6a1IYtZl1W2Vvs4DzRDiqVH7pSdjqOBYzcDU3pQenyntUl8jifrS6aeAewDfHm1m9u9Grc+VyLgBmqHzReLuay8e18bcOLUZpQQTNYZz1oBZ4+Ym1G2eo7dvoaebpmtDwvIZevsbe+1jD6Z6U/ZtZtvN3Gx3nzw0ytDmZRckAMnJmF6CmveVJOVcO6Wg3M2AaDT+OdF6SwrnLm7P7RbPlYGZdfH5koTPnydOr9LXUYDb4ptMYa7KC8a+SDxLNzQsVLYwE10iAEPEec31YIbP9zINmfXaS+Zvi6d80NDKC8bq2BZ/b6wNTYFurEN540RgSQQsH/CVLMO+McoClnxsnhYImGQwOaZXu9FvAkmSSpubKgJqkhadKhX4BWzZ9g6B8qV3vlViiLzRliS1UXjz5htGwK8PlqT0qnxVJtveIHB5wL/8+uC9wTufMnEErPmxzMUvuesTxCc+vOa6L953DLzzhxiam57sUKsI+P1jvoJl7dM2Vf+3hreZX+sYLTHas2xnhnutmUH2JxFIBP4NgSSpNIhEIBFoGoEkqaanJzuXCCQCSVJpA4lAItA0AklSTU9Pdi4RSASSpNIGEoFEoGkEkqSanp7sXCKQCCRJpQ0kAolA0wgkSTU9Pdm5RCARSJJKG0gEEoGmEUiSanp6snOJQCKQJJU2kAgkAk0jkCTV9PRk5xKBRCBJKm0gEUgEmkYgSarp6cnOJQKJQJJU2kAikAg0jUCSVNPTk51LBBKBJKm0gUQgEWgagSSppqcnO5cIJAJJUmkDiUAi0DQCSVJNT092LhFIBJKk0gYSgUSgaQSSpJqenuxcIpAIJEmlDSQCiUDTCCRJNT092blEIBFIkkobSAQSgaYRSJJqenqyc4lAIpAklTaQCCQCTSOQJNX09GTnEoFEIEkqbSARSASaRiBJqunpyc4lAolAklTaQCKQCDSNQJJU09OTnUsEEoEkqbSBRCARaBqBJKmmpyc7lwgkAklSaQOJQCLQNAJJUk1PT3YuEUgEkqTSBhKBRKBpBJKkmp6e7FwikAgkSaUNJAKJQNMIJEk1PT3ZuUQgEUiSShtIBBKBphFIkmp6erJziUAikCSVNpAIJAJNI/B/CW5XZyQ6BxoAAAAASUVORK5CYII=)
(i) ![](data:image/png;base64,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)
(18o = 90o- 72o)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 1
(ii) ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGMAAAAiCAMAAAB84ZduAAAAAXNSR0IArs4c6QAAALRQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmaQZma2ZpDbZrbbZrb/kDoAkDo6kGY6kGaQkJC2kLbbkNv/tmYAtmY6tpA6vJBmtpBmttvbttv/tv/btv//25A625Bm25CQ27Zm27aQ29uQ29u229vb2////7Zm/9uQ/9u2//+2///bT0a0+AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACMUlEQVRIS+1Wa3faMAy1Ux4pGx0pKd1YcLuN0K1A6Gvk4f//v3qlkJIEpyHQc/Zh6Is5sqR7JZtcC/H/2dO3ealpreRgXTUI2vw9rtoOu6a8YAhvNJLWdyH0LS+hJ4JJPvbxmjEjG17ejC7MIFpRtbJxdOJ6XCDorqPzaRlDzy65or75lGEIZrZjiSulxM6jLVv9pVbWdCY76zQ4PFsK4Q8TdyKICcbh5HgGm/4DTwEj3Yx6yDAwZndo/QJd8XCv+lMEakoTRD5W3eRqCqjyRLUaXH/GrEInDWbTNwjdtRCswQJhPrgTZ3g2aYGUX0bDAgb3DZtEtvP3BQS+gpD3Y9NfDi6PRJWZMZei8cCzjYU3m1WRH4cHnTtGJJ7cx7alXDS88ZiONL7tLX7SvOB5WGSx8QgU/A6fedG0ctAuTbB+VjPZXtLtHLy47TkfrW/hHvIF0arlYUlwhWktWjyS6R14tulusFWcuemMGgZvS5jvrhkCk3aqdt7xV/0Hq1J2vyW1oKvKb0ltatMAP73dMMv4b2lab6/4N8wP+rEX6PFB/2RWx9M+VaifwLvyXp9On8M/tpSX29CN6uckfEfe96qbD/Lb87w6p6pfkPCjMVjKyaDzbehXqvoFCS/Je+Mu3h4rIT45M6gcC4NRwhvXzhJIXsl4DYDBqm+U8IMxMmnllZ4krPpGCT8YI3FJcyd4S+AFh3Glqm+U8IMx6BUq+3jwrnDk9O5l1RcmCT8c45T5CrbDSOMDU2OUAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
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(iii) cos 48o - sin 42o
= cos (90o - 42o) – sin 42o
= sin 42o - sin 42o
= 0
(iv) cosec 31o - sec 59o
= cosec(90o - 59o) – sec 59o
= sec 59o - sec 59o
= 0
Question 2.Show that:
(i) tan 48° tan 23° tan 42° tan 67° = 1
(ii) cos 38° Cos 52° – sin 38° sin 52° = 0
Answer:(i) tan 48o tan 23o tan 42o tan 67o = 1
LHS: tan 48o tan 23o tan 42o tan 67o
= tan (90o - 42o) tan 23o tan 42o tan (90o - 23o)
As tan(90 - θ) = cot θ
= cot 42o tan 23o tan 42o cot 23o
= cot 42o tan 42o tan 23o cot 23o
As, tanθ cotθ = 1, because
![](data:image/png;base64,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)
= 1 x 1
= 1 = RHS
Hence tan 48o tan 23o tan 42o tan 67o = 1, Proved
(ii) cos 38o cos 52o - sin 38o sin 52o = 0
LHS= cos(90o - 52o) cos(90o - 38o) - sin 38o sin 52o
As we know,
cos(90 - θ) = sin θ
= sin 38o sin 52o - sin 38o sin 52o
= 0
=RHS
Hence cos 38o cos 52o - sin 38o sin 52o = 0 , proved
Question 3.If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
Answer:Given: tan 2A = cot(A - 18)
By complementary angle formula: cot(90 - A) = tan A
From the question,
tan 2 A = cot (90 - 2A)
Therefore,
cot(90 - 2A) = cot(A - 18)
Now both the angles will be equal, so
90° – 2A = A – 18°
108° – 2A = A
3A = 108°
A = 108/3
= 36°
A = 36°
Question 4.If tan A = cot B, prove that A + B = 90°
Answer:To Prove: A + B = 90°
Formula to use = [tan (90° - A) = cot A] and [cot(90° - A) = tan A]
Proof:
tan A = cot (90°- A) (by complementary angles formula)
tan A = cot B
cot (90°- A) = cot B [ As, cot(90° - A) = tan A]
Therefore,
90° - A = B
A + B = 90°
Hence proved
Question 5.If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A
Answer:sec 4A = cosec (90° - 4A) = cosec (A - 20°)
Therefore,
90° – 4A = A - 20°
110°– 4A = A
5A = 110°
A = 22°
Question 6.If A, B and C are interior angles of a triangle ABC, then show that
![](data:image/png;base64,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)
Answer:To Prove:
![](data:image/png;base64,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)
Proof:
We know, By angle sum property of a triangle
∠A + ∠B + ∠C = 180°
⇒ B + C = 180°- A
Taking sin on both sides of equation
Therefore,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
As, sin(90 - θ) = cos θ
Therefore,
![](data:image/png;base64,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)
Hence proved
Question 7.Express sin 67° + Cos 75° in terms of trigonometric ratios of angles between 0° and 45°
Answer:sin 67° + cos 75°
For expressing this into between 0° and 45° we need to know complementary angle formulas:
sin(90° - A) = cos A
cos(90° - A) = sin A
Hence,
Now we can break 67° as 90° – 23 °.
And 75° as 90° – 15°.
So,
sin 67° + cos 75° = sin (90° – 23°) + cos (90° – 15°)
sin 67° + cos 75° = cos 23° + sin 15°
(Since, sin(90°- A) = cos A)
Evaluate:
(i)
(ii)
(iii) Cos 48° – sin 42°
(iv) Cosec 31° – sec 59°
Answer:
(i)
(18o = 90o- 72o)
= 1
(ii)
(iii) cos 48o - sin 42o
= cos (90o - 42o) – sin 42o
= sin 42o - sin 42o
= 0
(iv) cosec 31o - sec 59o
= cosec(90o - 59o) – sec 59o
= sec 59o - sec 59o
= 0
Question 2.
Show that:
(i) tan 48° tan 23° tan 42° tan 67° = 1
(ii) cos 38° Cos 52° – sin 38° sin 52° = 0
Answer:
(i) tan 48o tan 23o tan 42o tan 67o = 1
LHS: tan 48o tan 23o tan 42o tan 67o
= tan (90o - 42o) tan 23o tan 42o tan (90o - 23o)
As tan(90 - θ) = cot θ
= cot 42o tan 23o tan 42o cot 23o
= cot 42o tan 42o tan 23o cot 23o
As, tanθ cotθ = 1, because
= 1 x 1
= 1 = RHS
Hence tan 48o tan 23o tan 42o tan 67o = 1, Proved
(ii) cos 38o cos 52o - sin 38o sin 52o = 0
LHS= cos(90o - 52o) cos(90o - 38o) - sin 38o sin 52o
As we know,
cos(90 - θ) = sin θ
= sin 38o sin 52o - sin 38o sin 52o
= 0
=RHS
Hence cos 38o cos 52o - sin 38o sin 52o = 0 , proved
Question 3.
If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
Answer:
Given: tan 2A = cot(A - 18)
By complementary angle formula: cot(90 - A) = tan A
From the question,
tan 2 A = cot (90 - 2A)
Therefore,
cot(90 - 2A) = cot(A - 18)
Now both the angles will be equal, so
90° – 2A = A – 18°
108° – 2A = A
3A = 108°
A = 108/3
= 36°
A = 36°
Question 4.
If tan A = cot B, prove that A + B = 90°
Answer:
To Prove: A + B = 90°
Formula to use = [tan (90° - A) = cot A] and [cot(90° - A) = tan A]
Proof:
tan A = cot (90°- A) (by complementary angles formula)
tan A = cot B
cot (90°- A) = cot B [ As, cot(90° - A) = tan A]
Therefore,
90° - A = B
A + B = 90°
Hence proved
Question 5.
If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A
Answer:
sec 4A = cosec (90° - 4A) = cosec (A - 20°)
Therefore,
90° – 4A = A - 20°
110°– 4A = A
5A = 110°
A = 22°
Question 6.
If A, B and C are interior angles of a triangle ABC, then show that
Answer:
To Prove:
Proof:
We know, By angle sum property of a triangle
∠A + ∠B + ∠C = 180°
⇒ B + C = 180°- A
Taking sin on both sides of equationTherefore,
As, sin(90 - θ) = cos θ
Therefore,
Hence proved
Question 7.
Express sin 67° + Cos 75° in terms of trigonometric ratios of angles between 0° and 45°
Answer:
sin 67° + cos 75°
For expressing this into between 0° and 45° we need to know complementary angle formulas:
sin(90° - A) = cos A
cos(90° - A) = sin A
Hence,
Now we can break 67° as 90° – 23 °.
And 75° as 90° – 15°.
So,
sin 67° + cos 75° = sin (90° – 23°) + cos (90° – 15°)
sin 67° + cos 75° = cos 23° + sin 15°
(Since, sin(90°- A) = cos A)
Exercise 8.4
Question 1.Express the trigonometric ratios sin A, sec A and tan A in terms of cot A
Answer:sin A can be expressed in terms of cot A as:
![](data:image/png;base64,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)
And we know that: cosec2 A - cot2 A = 1, cosec2A=1+cot2A , so cosec A=√(1+cot2A)
Therefore,
![](data:image/png;base64,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)
Now,
Sec A can be expressed in terms of cot A as:
We know that: sec2 A - tan2 A = 1, sec A = √(1 + tan2 A)
And also, tan A = 1/ cot A
Therefore,
![](data:image/png;base64,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)
tanA can be expressed in terms of cotA as:
tanA =![](data:image/png;base64,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)
Question 2.Write all the other trigonometric ratios of ∠A in terms of sec A.
Answer:SinA can be expressed in terms of sec A as:
sinA = √sin2A
sin A = √(1 -cos2A)
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)
Now,
cos A can be expressed in terms of secA as:
cosA =![](data:image/png;base64,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)
tanA can be expressed in the form of sec A as:
As, 1 + tan2A = sec2A
⇒ tan A =± √(sec2A -1)
As A is acute angle,
And tan A is positive when A is acute,
So,
tan A = √(sec2A -1)
cosec A can be expressed in the form of sec A as:
cosec A =![](data:image/png;base64,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)
![](data:image/png;base64,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)
cot A can be expressed in terms of sec A as:
cot A =![](data:image/png;base64,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)
as, 1 + tan2A = sec2A
=![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJUAAAA9CAYAAACk7SvMAAAHmklEQVR4Xu2ddah8RRvHPz9bMVEMbHzt7u78Q33tDkTELlCwW1ExUXkVO16xW1Es7O5EscVEsbv4wBx+h8PevXv2znFnd+eB5XL3znnOzHe+56mZM3ccWTICkREYF1lfVpcRIJMqkyA6AplU4yFdADgN2AH4JjrSQ6Rw2Em1EzAfMCOwLjAZsAjw1RBxIPpQh51USwSr9CFwPbBSJtXYOTbspCojeGMm1dgJpYZMqvE4ZlLF4VQmVQnHTKpMqkgIZEsVHcjs/jKpMqmiI5BJFR3SbKkyqTKpoiOQSRUd0mypMqkyqaIjkEkVHdJsqTKpMqmiIzBe4e1hmWYh4PMG7zPwqofdUu0HzAtMDywFTAS8C7wO/A0cBXw/8CyIPMBhJ1VkOLM6EcikyjyIjkAmVXRIs8IyqY7OcAw9AsfGQCCTKgaKg6MjOqkGB5o8kp4ikGOqnsI/mDfPpBrMee3pqJom1YrAej0dYb75SAhEiZ9aKW+aVLeGV6CsUmdJC4G+JNXUwEfArMAPaeGZe9MkAk1aqh2BTYHNmhxA1p0eAk2S6hbgOuDq9IbNdMCCwC/Aa8CvCfaxb7vUFKkK1zdbYqv8EwB7AJMDzwErAzsDZwAXhJ0JfTuZqXS8KVLp+nR7ur+URAK9Bzxc6tTmwA2Ah3VcmVJn+7UvTZFK1+eBF/9PCJgJAbPRJ4FTgN9D36YIVusnYIXS9wl1vb+60gSppgpZ3+yJub5JgeeBOcPGvE9LU/UA4PlUHiP0dc0p1KXq7vOZVgG4Jki1PbBFgq7PIS8KTAM8WiKOZ1IZX/0BLAv8VpNUewOrANvWvG5gmzdBqhRdX7sJXA54DDg0nKRXZ7KtwWn9XgXWrnNhw217eipgbFLp+j4GUsv6RprDiYGbQ3HW5KKIszqZc7E7M2ST7mlfvub1ndyjTptkTgWMTSpd35bAJnXQ6GHbA4PrckJ+rNkPT91bGlCHsliPVw6SORUwNql0fZ7z1A+pueRfFTi4i+KncdgJwDGhPOEbOX4+q0nMppr39KytmKQqXJ9Z33dNoRVJr2TyY2nhz6BTq/NKh4H6LsAboTxxP7AWMD/wVqT+jVXNwJBK17cV8N9REJHI64QTgb8FpgRM733Sr6hMqicHbwN8EbI2Y5c7gb9a3GNawMmeOSy/+L7eVS2shxngasD/Knr2B84LWWC7IcwC7AqcGCrw14ZxmwEa8KcgA0MqA96bOnB9RwAvAb4RXMjqYanEifk5vDq2J7BdmLBPAIPqs8LPvSqTr9U5HzgEuCNMtut7JwHnhJdDvdfcwMXBZfmyqCLJJbYubZ8OGGH/1VHUueyThHT1QPefgiRPKqvMTugjbdDq1PXNEIDXUrmYW5aTAff4SCo39rl0IlkkYCFe/zKwb4jd/H4e4Ang+ECgoq3JgkQ/GzggjOFeQAK3Esmi9Wknlh8WBi4tNVK3WaBE1/qlIEmTygVXnz7PFjC7sEDYSrQouqmNR0HUuo5xi/9V4a5KW6+9J7gki5PGOpKqiHmK5i61WMXeKHxxUXC5VsPLZyAYI+lOjwN0UWOVSYIug/PyA2HR050YxmdayhQkWVKtEdbvtgasGj8OnD4CYloEP05iO/GsAl2khNC6GIP4875ScP+fEARrqVpVqc8Na3RaUF2Wlkwy6TpbxVqxJtnFaOO2ZysKrcJrqSSWcWU7mSvUtbpNkLy3a6qjSZKkcvAOQEKZ3cwRftdaGd+UpXB9tjHwHk1cJjEdtzbkmpniupn1nstCEP0Q8EJYAG6lzx2lttXy+d8aHgwZ2Gj37vbv/psRXaOF3arMBBj/aWU3GOUGYqSb7JZULie5R200SZJUdtpY5Z1S748M8YRuriy6Pi1K4Y7aDVgw/WhRjNNcTtAiWs02K9Pa+PdnAmnM5tqJmd7bYe1OPU3J4SGOqj5Q3k9ii5MW04Jo1V031ad2epMlVbXTrvKb0u8GuKpfSKeuz/bWsAzSy4Gu36vbbFB3aGBt3OWOzJGefN2o8Z3EdCuL21eMody+UhW3vIxlotWrhTbjayVa3qK+ZVW9VR/+bWL1DakERmt0aliScJ2sruuTVKb+G7bYZalbsAygm/GjSzH4rloHLdlBIb7T4u0edGoljM/KUm1bd3INzi1LmBlWs9VClw+EoYJu0Mzwy7o3aaB9X5HK8Vt8NOaRXLo+P5KkE5FUVp3Xr+y+dPIvAQzCjRu0PAJjvGSSUM46LRUYuxlHKVqrywGLkpK+/OaO/fLauzvpXKWNW45NTIz3DmtzvcR7KlizVKrqPT0VsJuA0VjraWDxUBey5OCkdiKSyhKAhHEyjEMsPK4ZnvZyEOr3Wggr7YKkW9ESSLrbKjfTWpjOG1ddEyrw9vP9UO/qpG9FG93ZhcCSgK7TIN1M1L3tZWulVbWwukzY8y55XZR+ETD+/KDOTSO0TeZUwG5I5fgtNHqcoXUkidJJ1ud1EsmP1kRrZKDuRBjojlQDs2wgQZxQSdIuPpJcttU127bOVpYI85pViEC3pHKi3wyb0zp1fRnxIUGgW1INCTx5mN0gkEnVDWr5mrYIZFJlgkRHIJMqOqRZYSZV5kB0BDKpokOaFf4DK8aDTat6bWsAAAAASUVORK5CYII=)
Question 3.Evaluate:
(i) ![](data:image/png;base64,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)
(ii) Sin 25° Cos 65° + Cos 25° Sin 65°
Answer:(i)
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)
(ii) sin 25°cos 65°+ cos 25°sin 65°
= sin 25° cos (90°-25°) + cos 25°sin 65°
= sin 25°sin 25° + cos 25°sin 65°
= sin2 25° + cos 25° sin (90°-25°)
= sin2 25° + cos2 25°
=1
Question 4.Choose the correct option. Justify your choice.
![](data:image/png;base64,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)
A. 1
B. 9
C. 8
D. 0
Answer:Following is the explanation:
9 sec2 A – 9 tan2 A
= 9 (sec2 A – tan2 A)
= 9 x 1
= 9
Question 5.Choose the correct option. Justify your choice.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVYAAAAiCAYAAAAEa/HgAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAcSSURBVHja7V29Utw6FPbtQx8yq+1ID1rKpGKMb35K7lzjoboMxQ7jmdxkZgsKQ0cBDwBVUt3kBW6KpE2RPEHuTHgCeAYSy7u2tVpLloTstS9f8TWgtXSOPn06Ojrr9U5OTjwAAADAHeAEAAAACCsAAACEFQAAAMIKAAAAQFgBAAD6IaxJHK75fvwHHAXIEPt0P4yTNZPPgFdAn/jqVFiTOFinNEowGUAdIkqTvcnkkZ6ogldAf/jqVFhPTw8ebA/p5V6SrEo/6Hm/MbQSVrfUD2CHJNlbpcPty4PT0weqdl3jFXgKvrYqrIc+eU38w9eqBRIMvM8e3X3XtBOOI/oiJexPGh2/6Mri6fPib8p2xpm6OeoSr7rE0/vMqWWtUx2+OhXWjNyEfAjiZL1qsJPJwcpuMDhmJLpvwno03nm8TYeX6XhuPY/c0DB5eV+IWmc7O+ITEnyQRQFd41VXeHqfObXMdVrHV+fCOiUIvRKPa0U0wYifo4UFkIT0ZUbY1DlVuxD/t7pdSvY5vcna2iDk9/d54pvteFV+amrXrRunrv0mzzSxPTteed6VTFi6xisTn+i0qeNpVzlla68NR9vgq65P6/jqXFh3qffOGwSfRSWfRhzep+kukKHxBTB1CrfghIXHbpdHhHwknndT/p/cDOn25c746PHis8jN1nj8NAzo38VnyMa3rfHRRv1kjT7ykzMVCnJTFYE5sT3cDAnx/svtYv374eFzsR2L9Obsmdkk2s/azXbxwk+E7p7X7di6ttcd47vEKxOfZJE0Jee8f7M2k8mKLk+7wilX9ppytC2+mvi06bSTVY4rV3ubQTFDVXm2CmG9nTn3tgCN3hbhvOddz/2vwPwuJZD/dm4hK6KE3CfimE0XgYXdP+tsEqI9oW05tslk71E2XxXtdHKeurYrxbNDvNL1CRvPBvG+STkzu1mu42lTnDITVXf2mnBUcTpxylcbn8r46lxYc2LXEbTNBaCbu+KPC+mkvxE/UxCB0K9BFD/LJyNzruL5xRE2JdViH/rHNl27C/Kluzj/7DgO10dk9E/VZkFodMaTI46CZ1lEMJuf3Ea+HesnCjZfUT/eV/te3/a6Y1eXeKXjkyr/Zm2o91aMSE1yrK44ZQKX9ppwtCpgaIKvNj7VSb3IUo21aYyFhG5qYJ+ENTta+P4+SwkMBoMv/FFsUVgXdy6VzdwOWxERp30Y7HbGwppOOEtRyCavaMfGkB7TxMnOCRUm4Xo2V4Y7s43tNj5eBq+KfhQ+mfOv0Kbq87rC6pJT2vcUju3V5WhbfLX1qYyvPGabyq0KVbxrXFhFB7Ikf/r8N7pJaRVhs5xKmatZcOhdhTX/n9h3PiaVn+5idxxt/skfkcho9J7lrvg8VzEHVbk9Li8VRMFffDSgvRgtbG9TWO/i33w8qn7qxjKNqspoR1dYXXJKN3pqwl4djlY+vwG+2vpUR1jdpAIaWAA6ii/LRakIy+drhqPgIozj9Tg+fihztM2ilx0VRJI1YnccP2RHnzQS/7dq5xWIKumDXNsKq43tbQrrXfy7TGFtmlOqAMGlvTocVQirU77a+lRHWO9dKkA1hjySdSKsAlHyZ5vYYGq3OFnTXDA55/3AXwipylXmjnGSaEJKOkPbe5kKkPhEPLpWXgRZpAJccsoqFeDIXh2OnkguMF3z1dannUkF5ApdOHrmJJP6NVthZX3xuZlyB6RXrFQj//t4vLPB8q0uUgHZjsctcpbPnSbtg0+meTBdu5ldI1Ieq3Qu5LIylINktZyfg5XD0H/OnsN26/IyYFo2k7dhZS+yywAb222FdRm80vFJceHJcY8Vnxc321xELONpk5yyu7y6u70mHK2+vHLLV1uftpcKUNzeVhZySy6KXC6A2Zh+VNUHCmUuZSnVcPjdhbDmN41MuKf1fekEWi4AE2FdsLeo95vvW6gBrZgX+oMRlStLE9tIy1dsbLepClgarzR8ko2beF9VvtXhaVOcssiZO7HXhKMLc90AX2192uQXMqTheo1TFtDUAsgmMgyeDofe9yL0ptFZcdHj0/2ylpVcbwbRqzjeesL+ViGs1xJhvZYt+oiSM/7ZtgvAxG5WfsLlrbK+xRIVfozsIoH3D2s/zTuXr0djX6YIRsMLvo3KHhvbbepYl8orDZ/kfuDrpWVzoeJpE5wyF1d39ppwtGm+2vq0tTrWpjsD/r+w/eYVAHSRr86FVfadbgDQSGEYvysAALrIV+fCmit5V17TB/SEqDpvtwKvgJ7w1bmwFtFFD1/dBiwPde9aBa+AvvHVubBm0cVwdIFjG6B9rNL8BQHwCugLX50La9E5fpsI0AD7DSHdWkDwCugTX50La7YI4nBN9fYjALD9lVbwCugLX50LKwAAAABhBQAAgLACAABAWAEAAAAIKwAAQJv4BTb5gVX5H/7UAAAAAElFTkSuQmCC)
A. 0
B. 1
C. 2
D. –1
Answer:Consider ( 1 + tanθ + secθ)(1 + cotθ - cosecθ) ,
![](data:image/png;base64,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)
=![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Multiplying both terms, we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 2
Therefore, ( 1 + tanθ + secθ)(1 + cotθ - cosecθ) = 2
Question 6.Choose the correct option. Justify your choice.
(Sec A + tan A) (1 – sin A) =
A. sec A
B. sin A
C. cosec A
D. Cos A
Answer:![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= (1 – sin2A)/cosA
= cos2A/cosA
= cos A
Question 7.Choose the correct option. Justify your choice.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAA0CAYAAABvu91XAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAWHSURBVHja7VtNb9NIGB6XK5TrAh7fVsux9bS3Xe2lGCM+JA7W1olygrWQVVlsXeRDxSa9RULijMQB6An1D4C29LqqxH1XAvoDivoTtsnOjD322HEc23EcB+bwSm3yxn49z8zzPmM/Bnt7e0DE4oQYBAGYCAGYCAEYiQMAlgAAF7iQBGANjX7fuqhD6RCD9J8f8OuGvYsEYA2NbrdzBSHzT/Z/r43uAFn/YPX7FxcaMJ82DpZqKQZT0ryoadfeQBDeepsHMK7O2mvN/NLzrEuaDI4Aar2poxg6ywEYonbvTm0DgAfc84xrCMBj3e2t5FqdJrpL6qS1mt27cweMrCrLMi7/dlPeo4V9o4CR6/QHX/3U6Xav5P1dSwX7GOcBXmYDoLb25woYbcYy+MBmUF2A4RNJT83Ve+R8q+bTexHlRHQMRlXdhSRdDzlaTVDXEk9f5G868OrmfhGl6HmdqyoAJwC1X7cReI3BPul43tW5AnYTgr+YepKmAMwfsGEujt/SoBubJInJ0nXMH3GTeQ8BOIu+h2cKuvHSsL2f4seBZxu2/aupITfMh+pHXgX2XH1FAeA0Uol+oE7v9mQ6lIYkr9dBt6WaaXGykqKzqRxghOKgtuXmybV1uI0H7DwA4zwcRNR6lTXAEs2NZjkH/IA/DqWvClaDT4foC6HQYHy+EFqsS3w0BrC8PSyguSVGj480+IT/TQgYRMd6+49bjDV8+pquP/J0yD7zj0tW9K4qAEsARYSQqWm/E2qUZflvnjrjgMEz3emuxq7F0VcJPRapJ4W2dxgdhjUHtIiPu7NwgCVv9RARAbVHT7JEQl7A6D6J9iMpRnWMRmcNWCDGjgitGo4js+txHEOmq07Wj+rYdFcKWAuBV4kegwdTOo99FvSkIoBFylUaKGvaC9N1Vxyn9wMPxKwBwxNGjQueZNRDi82kxITqCutI7HkITbKVN2vAAjocJEUPr6broMVMaguXe3yvIs0MsKAfkPMZlnWZUWioxjAd3bfc66wW2zbQGoTvZk2JIR1C/TCN9sL6aqDFfBvnlOY+C8CCC/+ctg8jsl+KZP8wlP+K8u+sAWN0CHVne1xOXWpx4sa56MYyuWKgbm8XotGO/ouigH/Y+SBqPQtpSV9/EO3FlNN1vf3YcfSfyWesLn8/p5wm7wuyfVzRerKOmbxWWm+J41fWw0Q0L8QgCMBECMC+wThIffKQjNEb52Lw5hQpNxlGIk3AiMFbdEqcvExF5I1aKHHSMhWRPwQlivh+AVtE1+93C9iiun5zA1anmbTSixtjTJ3W9dtYIymJus2kVUZen2MR1y8FvGlGUraq5mEmrROwMq5fqvCaZCQNOX4OZtLxgmCUjiflTDKmlnX9Ns5IygCrwkxaxEjKAq/q5RtIecl7JaC6+dzy+pf4nE0VPuc9FiTHsKxllpNlTC3r+o3osKFG0rBBl/R1FH7ijOmJzt5R78Q5Ow6d4RB8TOYwo6jhda+RvCxjalnXb0SHDTWS1g0Y6w3kKTMTANQEqq8/Xte3HgQrZycth9w5SDJB1S9XNN5IWidg4Xky5HXYW1NyOCNM+F3VgDXeSFoUsGmMpMwkk3WeSbXgVYb7EzphIqJKwBbCSFoUsGmMpJUA5veXmQC2EEbSOVAipjTtyLC85TS16d9SAodpOR4TLGmUWIGKa7SRlKe3acykRUUHe8MkkOjUSOq/AIFcpDkPSY7jq78BbzZ1rfvX6d0Y3F/4FTzOmFqaDptoJB27cS5hJi3s/MVyG9POV1+ixw2j7NkQHRwIjkdzyOxHn/lNcJYxtQwdNtJImrZxLmsmLWMkJW9aamvKi+h8vmGUn7m+jIfP+L0UL/PjNYw3puYNYSQVIQATgIkQgIkQgAnARDQ7/gcwOLFLIjuNwAAAAABJRU5ErkJggg==)
A. ![](data:image/png;base64,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)
B. -1
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:We know,
1 + tan2θ = sec2θ
and
1 + cot2θ = cosec2θ
Therefore,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
⇒![](data:image/png;base64,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)
Therefore, option (D) is correct
Question 8.Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
(i) ![](data:image/png;base64,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)
(ii) ![](data:image/png;base64,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)
(iii) ![](data:image/png;base64,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)
(iv) ![](data:image/png;base64,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)
(v)
using the identity ![](data:image/png;base64,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)
(vi) ![](data:image/png;base64,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)
(vii) ![](data:image/png;base64,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)
(viii)![](data:image/png;base64,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)
![](data:image/png;base64,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)
(ix
)
[Hint: Simplify LHS and RHS separately]
(x) ![](data:image/png;base64,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)
Answer:(i)
To Prove:
![](data:image/png;base64,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)
Proof:
![](data:image/png;base64,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)
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DpJZuZmsMnmRo35kO3kR2LMxcGV8ZcQUosVBYvO/a5NNXM7xZVYlIC5V6EQLPqcLM4nGzUAq25hlVIwqOu10EY7JR7QcKExXNV2T33YrHkErmIXscizrXHQkREOle8jF5sRINGaFq40VguuIzGxb63T792RSb0usZqFLh6FkICex+jkWS4r/Eg7iVqFoFlTDoh6lY311mMe+kuuf4s9dyHxWXTWPQPEtKrv2PRb26trtcxF8wX2iRCZP544ZO93Kbhcd+m89kA++JfnzrVuk2Ad4j1bZN11LjAd01blwBwzBTughu4IZH7fQvLKUvYdI7ve7+6bjsCa+bb2mMIpB1R5siOjRQN43RjONfamsM1ixcjsInsICFCfrlpRiIy3rgv9nb7PmZcQtPCPcU6Mf27RdIi20OOx+uWXtP9tVw/9CrP1hbTkZxxnbD8TNX+dCcW+k1niSwBsLttuF+Eg88VbaRJgiHLx1hgLDqJa4LFYsyHQE9EazTVxcw9Q10WHHqdMXNmdxEhS1O9jv7LbdE1PrQ0cOKeUjbhhmRoK3Ji8RGJJ3Jr21j0diCbntOLuQc3cwOpspNzP2JpERo+hMjRKPyGGZLsPsiTgnQTnsOR9XBtaPKpU61ruznE+ja1oE5Tva9p65I5fKwU7uaH9+Ui0VjmB63H2vFdgsN1q4N8+C6I5uzHBOzTxzXzbc0xBL0tviWCN15wyHX2oc2avfS8xZrD+4zsGV4zR3bsxL0gdBxyyGwqFh5aC7v8TVmURe2w1Fg8uwhWdBSrikk+DV32rKXX9AVWfQuGZ3BljSJkCynrizb231tU5HRhARJFtW/peoup1Wh6P+0i5JaEsOeS8NEXBQU3wmph0710DQ78kcFtZZteh4tIzgoCc5qZsfh/brdOEntoeq/TcUOGunuQedmYaTuyKioMBtxku8bCbk1mT9aL7u4jyCVeR5pYp7iqtJnGy/zzoWbZGc3ZUouz/nzscJ/+wdR2Gp85d+Y2DE+dap0uygcbWRNiP0aq6a+5gRQra9q6ZF6fPIX7kkZWndUIjO/EpqSvS266Zr6tOYagP9u3mOXYd86mkBUT8e/RoUvaWHN4CUpV54l5XXqxQ5ZIzgJnQSNOFiUiQ/Bo3UFWTEaLN2Lk4yyaSRiyqKIeUdT1KDQnLA70PT0TsEVzGiKtHWuvYdF4n+ausVBK0DdqZ/SP7gip0DcLNheJUHmup2lk0Jop4XqLrhd2JCvTe2iDHZKPDhE1VwyXFhJmMZ/uYLp7UKj/rvZtq0sQTpTMVTfNEM0dhWgwF7NuGc/RDanNCIq+iZYSNWScuQQlN2ThQWLt5npE1raxsKAjfAgnN4S5Q3MjY6dxESXjfixO5pq5x42l3eaN67njkEXtGQmBMSWSR3K4xfaJrDt1qnUCelZU58wRrBsLhFP2a0Lxsaxp6675fPIU7rsaWH//fwRsKES9eje8DyylNgZzxTyyCfQucGV7Z/Yta+bb0mMIelu65ZIVm0uXO50lt1ttl7S55vASlK5WnTVz+dJavkugfJEHWZx+ZtDrmMisQXQhm0zR+1zDZCsBG0vAnEi4kyh5aSycFnrh8kjdpnDxJf12D+JkWaGXFKHDSBfiJ6v0NnO8SIilJvtNdX0EEDvPmitw8+FEQDa1BflkYqab6YQOwUV+4D1NL75rLLQH2XNtt9j4cCOq2jElfu7n+QiVfuyTonzJ2PQ6p061bo4gbwgfzLeJNNe0dRsGJ03hvmZwTlhXWgzEwrtGF3jsVPfeZYSFFcS/xr4foDl33EuHyjdXXqsxGey+MK6Zb7uOIZi2wTfBN8XaMKazWNrWmsNLkbo5xcuNOJeX93BDzUOSHZFOsijvsnyMTdvnmk0gcGmwXrAW9A8CRimCiviNC2et/58lxaLP3EpIyyKyKeT9woNTNygECoErgYBNAYJuoWCBZHE7VvGNlkfL2Wksl/2bRe9mg8DKuqnYiBEDz51deKz213OuFgI36ly+MIqHIjvuS4DsxZzm19nU6H2u2QbAQ5vVxdlPXS/EqkPAbHc2RvksAZLIl0nYsQZ2WFwn9CNjVuIl96k6hUAhcOMhQJ/Ghc+tuMmCfIheSWshqaZvzahH8x2TdX4uylM7SBEQIUlLNwWZHKK9dc+rj8CNNpcvBdFDkB1WDy4joaY0P/dsL9s2K8o+1+wCwG4IKenJ2rit+IWp/Z05tLaIEBI1JELIDgvJ2fdMrbXPrvqFQCFwfghwBwmk4MKdZtgWGMDaw/U/596lebOhEwxSpRA4NQIXmcuX0vZDkB2RAMSVvXAdsYhMzz0aO7DPNbsA4HJyoi6xJ+Ec/YPkbXPZgnfdy99pRxAdpI1pmBn5mDu8JW2sOoVAIXB9EBClZLMmi7lopV58t0WU+q7NkR2/ZxGaituvDzLVkxsNgX3n8qX18xBk59IaVzcqBAqBQuDACPgGcm/TMtDjIQqPa5Fx9Hg2a1IAyBPEjSXi098V/08XIw0Dka3oRBFQclgJmvA70XX7HFDruVzljkqZHunivqIaaRGlbahSCECg5vKWeVBkp16SQqAQOGcEhPwjDkhJLzR9MoJLF8F6K5cLrR794Zh1XbSgHauQcNpAf0OcHtwIEde5qClHgdAwrimkALJrs+hMM48jP1zx3OiSb1YpBCBQc7nITr0JhUAhUAg8BQKsL/K6IChTEa8MxM6G68cWCOHmOpo7YoabiRVGfdGfY86qh7eUG+qscXs7s45lSeQX0jMWIfDIlYShFQ1aExsCNZd3zIOy7NSLUggUAueKANcUIiGL+TTJKYsNAtNzSfWM6XNkp/+N9lDSzbGImpK4c3o+3S7MWW0ci+Lg26kbzDl63FfaIiS+SiFQc7nITr0FhUAhUAjMIiAK1EG8zsmTN0s+Gv/K7u0Yk7EsITvcXz3NRb8W2XEtYrLkcEvX9eNXnDs4PfNOIlPZk52j5giWJaeD1/BffwRqLhfZuf6zvHpYCBQCeyMgalOaClYZREIRsXmPFr3Zb3xMsiNMl/vKIcfOkxsLQvXIZo0Sfl6lEOgI1FzeMhfKjVUvSiFQCJwrAr5/fqSTcCSDyCfWEnoZImAC5Z4t+Zhkx5EsBMg0Qs7VG4vjIoSVO19uan0613Gsft88j2suF9mpd6EQKAQKgadAgNCXOHl6dhTLiugsbi2iY+WYZAfxelRzsd1vaLWz5biwHKvjMOUqhUBHoObyjrlQlp16WQqBQuBcEbBAsJTIlTONlLpby6PTycYxyY7xeEg7qFg4cS8PaPl/7jRzaO65jmH1+2YEai4X2al3oRAoBAqBWQQsEKKZ7jgRFtsEPijJAwc3ljpy5RAMP2ZyN/l3RHNxLz1i8je6GoeHEihLOLi0yO3jiAjERrlDC2uX4PDxS29S9c4GgZrLRXbOZrJXRwuBQmAdAhYIId6sKLdsyQVlUJZT59FJhHhLHOi4G3Vvm+Smdl7VvVpWZVmT+99ESPm5eyMnjquRHJAGxzlVNDj3X9hEriz3Fh12q0aY7p3kCQuvr2rnhUDN5SI75zXjq7eFQCFQCBQChUAh8OQIlGanZkQhUAgUAoVAIVAIXGsEiuxc6+GtzhUChUAhUAgUAoVAkZ2aA4VAIVAIFAKFQCFwrREosnOth7c6VwgUAoVAIVAIFAJFdmoOFAKFQCFQCBQChcC1RuD/AHq7VZ9gq70WAAAAAElFTkSuQmCC)
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Since, ![](data:image/png;base64,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)
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![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= RHS
Hence, proved
(ii)
To Prove:
![](data:image/png;base64,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)
Proof:
LHS =
+ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Use the identity sin2θ + cos2θ = 1
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 2 sec A
= RHS
(iii)![](data:image/png;base64,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)
[Hint: Write the expression in terms of sin θ and Cos θ]
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)
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)
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EgyFwdfX0WzZymcvx/XFPVN0V9/ZfnbdePBH2i4vHXTsOSnYFEHkbQfQmbtG1Akgegu0uwjJVrlRxzkmPfXNbj6au7jXnfa57194q9a8zDAFosS1mDqVvDV886cuzTl9StCoFWybHksThUd0uGw697CZUUi1V1jcj6Qpglr7kiatBowksDdwizpAQkkUgimjIlptov6TjMbzQoyPNT64Cg/SQq79V/kbcEz9y8IuIaCyNT3cHqg/XEnroYnKRcmpt/VpHjWLmGq+ZmNZc676ukNlJas7074fdvBsvsTy9hDaZubbYMUrdG4tcqOZ4kvrr15RlMsqqUsZcv9L3q6j90R2g7+uVKaoQ+w5L6YPuS4cfiK9+v/WJ+1Oz62GoAhr2b7nGTaK8emySrKa34IVeNe2j/5VlvdjBi9ULAscAtIvCmfDDol3zNCr+o8jhOTcYeSqCJVYJVNs3FY+Qauaz2XX2p875KYOdMc74fbMVfvm9gJn5wiWswdWuzRZC6NRK/VslRMTQB6Gvwy7tbHLfmT4no60EW5vR16/oS8Ktd/9ZDwiRp6oXRmiXKtLRteLNmUV9q34h/dCf207i02H/SvGNaxA/DF9o1cZbDkQ2iMXhmVRnTvwu6nM5zH8C/3Ql6zmspBhFp5vWQAoOTSimpJgYoSZCXjOffEzvMMXKNXFYbVV/ivK8S2A8Wd/RGWbdWlrgGU7c2X0WpWyMwbJkcjRDVn2dEaCErRTOKU4LwhIRPhawGzBgZWNc1aMY8M3MPTWcoeWZ+zbsDM72jHAwg6Xl7gsEsNfEY4enLzShQidAgFCMPJVd9gKuKfkhTSfRl1ibXUndM/x6zpA/hvoGFu1XzLvWDWozclfj8211hXa4eQTyaVCVNg5WeHjLvR64Ry2qjqkud91pofduuT/3cUx9AvxG48fBS12Dq1mazn7o1Ar+WyVEx3A1pFnWXIxmZeyihGWXXNVV167prlFzNkayL5kZ3h5pNz1JFd1rP4+DqIj4S8VnD72nQi4S7LqFb86W7BtMl3GV2y5j+fdaxSvoGJWn2dedXiuRpMI674mM6HTkOA0E81Ud/o+ZUI18t+5FrxLLauOoS570ILbauEf26pg+1WJa6BlO3Nl9NqVsDMWydHAeK0Vw1b+qQwE3BMHo1y+FBQB+wHzSeH7nXkYWHB43pJU3dmh7TpbS4Vd1KcpxvWWjC8Mi3W8WOd76esuVWEHDO3cVrbdDKkWUeBFK35sG15Va3rltJjvMuB31PRorqz2zxbM15pT9crZtS43F/fhD94nCJvhNpU7d2AvtOOt2JbiU57mSus9NEIBFIBBKBlhFIcmx5dnJsiUAikAgkAjtBIMlxJ7Bnp4lAIpAIJAItI5Dk2PLs5NgSgUQgEUgEdoJAkuNOYM9OE4FEIBFIBFpGIMmx5dnJsSUCiUAikAjsBIG/AU/vTKodEyWAAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Use the formula a3 - b3 = (a2 + b2 + ab)(a - b)
![](data:image/png;base64,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)
Cancelling (sin θ - cos θ) from numerator and denominator
![](data:image/png;base64,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)
![](data:image/png;base64,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)
As cosθ = 1/secθ and sinθ = 1/cosecθ
= 1 + sec θ cosec θ
= RHS
(iv)![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAAkCAYAAACkATUaAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAASMSURBVHja7Vo7U9tAEF5DC6Em43ObNuhMScfICnl0momtcZOHCg+jYQIzKgiR6UiROo8GSEmfBijThB+QCUn4ARB+Agy5tRA6yydLsiRbhmNmBz+ks77v293bu1vY3NwEaXfLJAlSdGkjEQGgZNvmtGk6swB7E1L0MReT2ST+73ddu6ktzGvGiqHNrxDa+DAy0dnfRNTDFsn0Drn5R0kSa69qDytQ+amtth/Gud62m/erFe2zubU1lSdO4aCWpZcVIEea5cyNg+BIlgJwArSxO06OytsVe25Lpa9os/04b5xdbxynOcsG/c0GvAQg51GiR/0wl96uzffQq57v3LF677mKBOfU6VOgdB8ddbG1row4ld9g5dN74HUXbuRiWaWvad15ihk2b5ziwS1tjgA57if61pY5pVJ1o18qWm8tUgJwxoBcoJXK2iFejyBbKlnzPmcOdsZAUCQgeA9Rl1ejQDQo7GKEGBR22PVroxBdhNWyFhc8Hj1OVZVu+Ljhcq6+8czSyJtKpfqtWq1+rFYfvQ/jNCucuYnuZg1/iuhcX6l+ajrO7DIKTh7te/e6v6cc6eu6okDpxEtxOAal9XfRqV05wHHbTfoYrh1rmIKHYTUsbalbdDgHauzczPkGfQJAT/DZ401h2eBMLPqeW+BNmqY+w0R3dNOcAUFx0REM4A96Mp+qPYKuI3vSG6tGyB6LgndJwbgpzyWSG1sZtuhCrByPIk7jBFceOBOJjh5cI7DPp6eb17Sx3bsUYR7JXYspCT2WYjHC3+ulckK+JxEdp4OGAl95sp+z96NI8SKsLOUrWYieNc5c53Q++v0xjSUK5AdGeg9xLN2VyrVD07an/THCCzmX1NK/oPMExxhOISfAamgvsxA9a5zCJZtblJBjNwWL14Rx5nRaUb946R+XgSg2rllbrHApEe3Anxpg0m7pD5pWc4FPk517qBE6p3dqA26O5FLtX6yEh5reRVgN7UUWomeNM2zJ5nsUqe2LhEXRNaq97RfprNrc5sfi16AofLfnVk7RIdwNDTgV3SOaakTfd35XMN3kaSKs/OaMaKMmzuZNHjjlduld3B6+i6C9FUivFWsbV4qekQlWIBf9ViC3XnSx94+3pY3028hDEODFbbO0kX4beZCFjSzkpEnRR2xFa4wYh8aSOJwV9uGL1BgxLo0lcTlL6/m5NUkUoTEisEsZq7EkOWc+/u5VRXe09uM6KWepCMmzSaIIjRFdhCY4Bk3CmYffNvV7tXLpkD9M0U37XhTXg3CWMgLyaZIoQmNEHqK7uHrxe0en/KEKCodpOorrQThLJXpeTRJFaIxIKnqcDZ9Op4wAf/gJnHKEIoZxPShnqYjIo0miSI0RcUWPu+HDMuBqMtH9z0Rc83VSEs5SFnLZN0kUqTEi6/SOwonwXx+x/uIj0+XBjfRwrt1nScpZuvSeQ5NEURojgku2OI0lSadEHj+ejU/Q+q7HV51O7HpZoh/Xg3CWioysmySK1hgRWLJFNpbEivYQ/D1TROA3wrgehDO5LSm3YaVJ0aVJ0aVJ0aWNqf0H5WogWlZUqO8AAAAASUVORK5CYII=)
[Hint: Simplify LHS and RHS separately]
LHS
![](data:image/png;base64,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)
use the formula secA = 1/cosA
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= cos A + 1
RHS
![](data:image/png;base64,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)
Use the identity sin2θ + cos2θ = 1
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJwAAAA5CAYAAADDaUIQAAAIxklEQVR4Xu2dd6w9RRXHPwhEQREighoFpSNNLKgBwRJBirQEpUkTRBER1BhjQywQTRAUFQIK0gOK0UhvEnqRriAgdiIWsIuKNZ94JgzLLbub3923+96cf15y7+zOzJnvPXPOmTnftxhFigY61MBiHfZVuioaoABumCDYCHgd8EfgQuBnQ5lGAdxQVur/41wSeCdwGXA3sDZwCnAx8DHgP32fTgFc31fo8eN7K3AdcE/28frADcC7gRP7Pp0CuL6v0GPjWxw4AzgNOD8btlZPwP0NeDXw7z5PqQCuz6vz+LE9BbgVWAbQqv0h+/o7wErABgG83s6qAK63SzNyYJsBTwMuyL4VgLcBvwRe08KP2xzYEnhfF6oYCuBeAhwF7Aj8vgvFDKgPwWKkugtwdsNxC159QsHqe2YufQXck4B9gTWAdQAB51jXAx6euVaG08HSgNupW+27Wli3/YCjI+LduAv/r8+A2wt4CLgS+CqgQgrgHvsxuHaHAysCBwD/bPg7WQVYC/hiPKf/90jDdzRu3lfAVSfyjQK4J6ytIFsZ+Cjwr4Yr7w6yG/A14BpgNeCFwG8avqdx8wK4xirrxQPbhLvxeeC/MSLdjx/X3BbdLX4N/Ai4CHhDvO/+Wc+uAK6dhtWbfqVRodbCPJjO96gcmG1fGjkye9NFuCUDShqBDrw+lQBaLrM2rwr/LAVLrwDWDTcjgc13vCXydPlno2an37cV4K6hmNvT2vnem9qpo/5TBXD1dZVaPh84PiyDfx8FXhRR4mfDcqS2q4efdRZwXgQ+bwR2Bj4MJIsiaD0l+DRwbzYkc2vfDAtksKTfdVKANgfWEuHDfaLGdHaIo7G/RFv7/ACg1czTLTVe1bxJAVwznT0LuAo4Hfhk9ugmwLeBM4GD4vMXRAS5TwAk78mDdwMhTwZ+Ctg2+an/qAzpMOALwJ+Ay4FNxwz5HfFDmDQjfT5Bq5VNcmAEDm8DvtJMHc1bF8A105k+055xaK4PlMRtT0skOL4UlkzwCSS/q261WiS34B8ARuPPA+6KXOORwF+zd78SuGMRnCC41lpWA4X8kH8n4OsRfHyqmTqat56PgHMbchE9e2wjLu63Rjyoj2VG/7cBokk3M54TYPIWh4s8SkzS6qwbHf4KcDt+D/B34Mbwp7Sa147w99rMS2u6B/CLysO6CFrhU0Nvbd5d+5kCuCeqahzgBPLPgSviLtokJb88QKO/ZQJ7lOizefsjOev6cbuG8+8Rls69osU8pEXqI+9zKeCIyvlr+l43wRSLFwL0L2cq8xFws1LYs4EfRoRpdDpJjGCNRI0AjR5HiT7c3hHBurUKsHSKonU2Kevdt7cDb44tu+3cHMPVYy5qup3/JCyq/uFM79QVwNVfQq8BmSQ1ZSGgcj8rveUZcdabDtSNOLce04URoaB6MeC29lrgmEpb1+cEwEDCo6s28lxgO+C4MQ87n+8Bf455uaXPTArgmqn2TeF0vz4ixvxprZKpDo+bDBLeD7w3rgzp9+WyAnAn8DngM3Hd6NgAXfXUwO3uqYDBRFNxfU15CDavo4+SJ4c19sfi0eHvmnbSpP2QAGfqwYTnXB7e62cZiZrL8naFtyySeFtDH8/oU9Eiek5pvsxUSTrr9HPTHOpeq+Xn3m8TgPp0brVJBIN+4Edi22uytrY1kWyk7PPjxIj5euBlkTIxTTMz6TPg9FuM4J4e0dPyYV30dzT/WgRvuc6FaOEE2INhOcyRfT8DWxqT+t0WMIhwCxZ8WqvvAudm0ae1CfpZRqVusVobgeilS1MWeTJ42nyNpg+OYMQTBcco8E3p5Dk+t32vpZuX2z36MpVzH/Dlyo9pWp+1v+8z4GpPojQcjgYK4IazVvNipHUA5wVIk49GM23FrU8fwdK2IgtYA3UA14V6rKks0m8NfHxRDK8AblFocWG8Y14BbmEsWZll4RYpGOhWA3W21BI0dLsm87q3OoCb1wook+tWAwVw3ep7wfdWALfwINAptUNVvUMGXKF/aP5j6ZzaYciAK/QPzQFWfaJzaoehA67QP7QH3ZxQOwwZcNWxF/qH+uCbM2qHArj6izSfWs4ZtUMB3Oxh5EVRI0Gr7qXRumRCxZVtvTnsdmfbSyewIMkdskUQElrIbCnhNFoHZzun1A4FcLMDnAsrk9GyQdngdfNVo3BaOoW8OMW2XlU3avQ7a0WtBDs0KrlyGny3ww9G7aoV/1JLeCV9w6glnTajOaV2KICbtjztvveuoD6lV8c/lJXaWfjidW/BYWW9ktpKHGPRTV6WZ9WWFVwyfabPvcqeCG3S6KR1kCLV/9eQc/1WRz/n1A4FcO0ANekpq7X8XwnWIljUnEhiLE6xuNjaBOszJPtLbbVQ+lXVUkP5PazksnzwgejUd1gvYfVVEusTLGC2FmEca3kvqB0WKuBmRf+gPvWrpHTQ4shDPElSW6u4EvNk3l72I7dl2SitFVUsotk+2JesrtLPkx1gmv/WC2qHArh2Fm4c/YNvOycoEgSJFU+TZFpbi6Otfl8zqq18l1usFfyWSSY5Gdh/QoDRG2qHhQq4djCb/lQqIralpINVqq38DdPaGrFa82F9qiQ3VcoFqSZkUvK0QC43eUDyfxCS99UbaocCuOkgatIi/bMOI9JxtPPpvFrAmfoY11Z/TMvle+SBM7gwYLBWNS+41nrdHOQ0Wr6q9IraoQCuCZzqtXWbtFhb/2yUft369Lvk3zWStQC52lZwWRknTZhV8vpnFnpL81D9/wumVGRwkgasWiXfO2qH+Qa4PtA/mPKQjFAymhwAz4ztT9Lm20Px3nARdHlb83ZSd1ldb/Va4hYxgJAPxFRJookwJ2e0KvPAqKCjd9QOQwdcX+kfrLl1S5T3xMSsuTFBYoSZ0iRJ99W2WjcBaw4vF7dOrZipFCm1BJliO6m3kvSa2mHogKu3yZVWvdXAkC9g9lapZWDjNVAAV9DRqQYK4DpVd+msAK5goFMNFMB1qu7S2f8A8x/6STUcYnYAAAAASUVORK5CYII=)
Use the formula a2 - b2 = (a - b) ( a + b )
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARQAAAA9CAYAAABspJYzAAAPTklEQVR4Xu2defB/1RjHX9m3MGSKFMqW7MkaySBLZMkWspaIQowJyRITk50aEkUa2WqIqZQmIktRSKLSZktK9rLOyzyHO7d7P/fcz/d+Pp/7+X7P+ec3v+/nueee+zznvs/7eZ5zz7MOpRUNFA0UDQykgXUG6qd0UzRQNFA0QAGUMgmKBooGBtPAMgHK5sBzgb2AfwymgdJRjgZuBewJvAn4Q84FRWZtamBZAOV+wKuAnYHfr01TLfyp7wm8AXh+scHCbTHaASwDoNwO+CTwZOBXo9Xk2hjY44DnAU8D/t7xyIVRLnZOLIRVjh1QrgMcBXwU+Oxi7VPuDv+NuX0MOAt4+wSNFEY5jukyd1Y5dkB5KvAKYGvgqnHYaFWO4hHAoyJO0vWAdwROAB4MnN8gXBhllwaH+T3XZn1Y5YpHNmZAkZ2cDHwQODTzSe8NvAt4InB55jVrXexGwDeBXwao5Ojjc8A5wGtqwn0ZZbFXjravLtPHZrmscrqR1K4aM6A8EPgyoC/+i5anvQbwAuAOwF0AJ6jPdFfgd4NoaPV38kLg3cCPAXX+z4xHNobyNuBetaxPF6Ocpb0Es9cC7wD+kvEMyyzS12ZdrHIwXYwZUJwYWwW1bpvkTtDnAJcCJ4V/70tRACVviuie3An4QIjfPfNlvE0AkHT6q3FtDqOcpb1uDpwB3B+4OO/xl1JqWpu1scpBlTBWQHHinQj8BHhRjydWaQVQ8hSmjncEPh2u5abAZsAlGZdfFzgN+BSwb8jnMMp610PaS0D5EXBf4KKMZ1hGkZXYrI1VDqqHsQLKjYEfAu8E3tfjiYecoD1uu5SiAsBvgHOBY4Btw3U0NpLTvOZKYPsQzmGUBVByNNsusxKbNbHKlY2m4eqxAsqGMdF3ihU098HHCiiunkblbw98Dzhuwm5fZc24SG2V/cqEPR/Gjh4JGKTT5fs28O8MZd0AeDSgvmzu85GtmO79Tsb1ipjG3wB4SMgvmlEOyVB8L4zHPRSQFXwrAtdNrreyW0QmUlVoB9lb3Q7ayNiHf79phQnq1r80I4mwUps1scpMU+eLjRVQDCKdHdka96HktrEBipNgb+AmwH7AhcAmgEDp//9WeTBl3xjg4G/Sdie0u1P95OCCiqyT3E8Qfg0cFin1uwHuO/h4hrKeABwP/ClkvZ8Zm8dGIDyjCw4GjLk8AHDsi2aUQwGKK/mHgrX5r9sV7gE8PRizrC41F4i3hut3dCQEtouNf6+LTJiy2kt9qWfndWobAUcGO+xKIgxhszqrzLFzL5kCKL3U1UvYVUiA+25kH/4VV+8P7BEv/5nxtyQrO3AiJll/1uVzkpsKT393cqeVLQ1q19hHsmXH1viNg/24kqa2WwRm/bThI5lPWQWU9UfAKIcAFJ/jawHSb6no4UHAF4DDgZfF328bAWl3Dld16c8PiwSB+6fcq6NsWux0E6vNReT9HVnJoWxWZZXVOZZp8m6xsQJKcnlMCUvHc9tYGMo1Y++MaVXdiMQErgV8KVwYU6ymN5OsDEMf+c+1h/Ulf09kY1L2wj4MQFb3gbwX8IV45oTUr/Y2OGcgtjqhdgA+E2wqBVm7dK6uvZ8ujyv1ohnlEICiDmWPd474UtKB4C2T8OV3X5R6FFwECn+ru0La2b097ig2C3lrwMXDPVIuKFUbm5UyO/XXFoUPabPqIjCTD2zHCigpKOv+CF+m3NYHUKSbGtsXeprmJGhzx4xrHBuMwUk0qSVZV76Uvq3KvzledN0L3QqbL7/BUGn2KRFncTxd8RNXzGc3ZEFkQK60ukvqJKcZ2xEoZU7zcFFvER8mXq9lcLpdLwEOAq5okfElkoFV3ZYkaozj+8BvAyQmreC3DLDQxgJ0UzsiXBkzZ7qmJhjc9a2ba6xLNirr+UaH3Ya02ZoFlJQ2/nnED3ImuDJjARSppb60IPDTjsF3ybq5z23uvrTp40gBQOYmFU/tEGCXCQHc68dmtKavtWUaLw725Li7mgE+A8aOwQ1u82CUswYUFxhjXAaXdVkmNVPTgoLfmMmim5ovr19mp0C3c/oZwLOC1QmANhnPy1uC9EPaLL0fiVWuKZfHh190GrLrpWr7PUXT/d3of91nrl7XJSuNdwfrD2K1q08CsyxSZrMHBlQFA92hpuZE/notuJvkpOSCt6um4NU12cxA6XLJrlxh58Eou+yxUpdHXf4sMjQGwyc1M0BmcgRU9drU/IjSYLpzQNdHAEmBV1mxGwplVO6z0v3Vpaq3IW1m31VW2aXPqX4fq8vjw/iiqAC33rty5LQ+DCWnv2lkpOSu3o7Z9G9TS3pPK32brPEQmYf9+EGewVsDslJlv71JzZXs1GALTTEnGcTjgQNbxmO/ulN/jHRpNfvUdIk0X1fMl0W3Zx6MsssWKwWUa8cGP3UhYNRjWd7/ZpHeXTfcI+NGj2kZmMxS0DCOJqPcpmFPlfPgw7HomDqutqFtVmeVXfqc6vcxA0rayq3Pq9Jz2hgAxXHqxrhqu4LXmzrXNREszws3zQlal3Viu/obp3l9+NkHhGsiqOijp+bqJ1X3Ra9/Aez9DN4KJm2xhcSUfGH8bOGyDmV/PnYx++1MaotmlCsFFJ/jKRGwfngAeFUNsgozcKaJDcK+GnhluLXGXapN90xWafzPYx4MuGs7QaUeDNXVvGEEa1Mfs7BZnVXmvE+9ZcYMKD7Mk8KIxgq6Vk3lBRRlZTVdef3eyupxgftBpLBOoOoLvl64J+4HOD36czV03FVZ963og7sC7lOZhLICQcFUcjrgSHYgYMgumoK6ukNmIwSltmZWwuDufSKl3HQsQbrWWI7j1zWqfrQ5LaMcyl5DAIq6NJPjng9ZYZUFCuIySbM3NhmN+jYQbkA92cO/mwb23ZJ1+HcBRYAxpqIrlJpAbhxG2+hypja0zey3zip7TOd80bEDisZxNTTN+YmWx9L/NJIuIzBD4cRSXr/Vl8yVoS0ll6+p/pK+nLosApubowyGOrnM0KQ0cuq1Lis7EZDcw1JtujZODFdL4x4+n0054yOpmbFwr4sBQXfEGsx18psWrcZ0ZEa7B4g4Vt0106EGks2WVF8o+3a+CHRp9a2OLZdRzspeQwBKeh4ZigCi3gRwz9E1ZpTAJMmpDz+QNEiriyS4yDa0xxcr2RvT0MZDdFV1gWSCzgX17Xxw4ZiVzdJYm1hl/1ndccXYAcXhu7qqdCdiFcUHV0bpsFMDvjwCminmpiMg+zLKzhv2EBgSUHrcdilE21jl4INfBkDxoXUh3LnoHopySPXg0yCrQ20gNZeOt9kgh1Fm3WwKobVyfEFf1UxilX376pRfFkDxQURZU2zGC2ayy69TW2tXwAOP3ZQlqHeV0VgUo9Tl8rsn98Ws9gOW+szELlbZp69O2WUClM6HKQKj0UBhlOMwRQ6rHHSkBVAGVWfprKKBwigXOx36sMrBRloAZTBVlo6KBooGCqCUOVA0UDQwmAZyAMXT5N2x6d6IaZv7QNxr4XcppRUNFA2sUg3kAMo8Hr3rs/t5jKHco2hgLWtgECwYpJO1bIXy7EUDRQP/10ABlDIbigaKBgbTQAGUwVRZOioaKBrIAZQSlC3zpGigaCBLAzmAktVRESoaKBooGiiAUuZA0UDRwGAaKIAymCpLRyPVgBUbPSxpz5GOb1UNqwDK8pjTk90syWHZisuXZ9gLHamHFnkokgdFtZ3vu9ABrrabF0AZr0U9jtASDdYvNjAuoGgvz3xd5PGW49XY1Ufm2S3WdnKHtkXUmmoTL9PzjH6sBVDGayIBxSMtL41Sl55F6ktRACXPZh7K7Knz6ZxdaySVc1LydDe1VAGUqVU39wvHcqL/3B98ihsKxjvG2cInA5vGucOXTNFXuaSHBgqg9FDWgkULoOQbQCZnudFz44T+bcN1PCe/iyI5jQYKoEyjtcVcM1ZA8SxXMykWTLfA2XETjuhU1uCo7oiy1iZqOuxaDRs7slaRgdWTovRnzkek1ijypH/1ZbPwmWwllQRdjPXWyF0LoCyPoccGKL64ewPWENovatZsAuwU/6/WUVLWejeCg7IXAZb79AxYy3VeUDGD7speUWD8sChBYl0bjzO0mHtXs6bO8ZVSJd7Pc4gt1Wo1v9JmqIECKDNU7sBdjwlQPBvH8Vh/xuqBqRby/lEPyJf/zHj+JGvdZCvvVesmW7DMMp2mwtPfrYezVRTJSircNfaRbNlR9WDjYD8ymtR2i8DszoBVKEuboQYKoMxQuQN3PRZAscjYoVGwSjciFS2z+qCF2nVhrKFkRiXJyjCMa9TrBfuSW67TbMzFoS/7sKiWrCI1C5StH4XT2lK/zmVrBlnkrQpaO0RdJ9nUvgPbpHRX00ABlOWZEn0AZaNIOftCT9POiJrKTdca1zg2GIMb7Sa1JGupzqYyqZZW9UU3pWuxdptF3bYHjo7yqMZZHE9X/GTrqNukO1VtMiALk+kumYYvbYYaKIAyQ+UO3PVYAMVC8NsFCFiydFLrkjWmYY1kT8i37KdNADCQas3j1A6JAvNtAVxLtFqPp6kAmczGguQyH8dd2gw1UABlhsoduOs+gDLwrf/XncW9T4v/bVGrk1y/Z5esGR93sFon2bRu1U2xrw0AC7C729WAqmAgKDQ16wZb27ka3E1y1oC2hK0xHMGrfp9Z6WpN9lsAZXnMPgZAsbi36d4LJ3wbk+aUgDJJ1uLsMg/TyCfEIegGZC0oXi3SLvs4NRiIzKXeNgQeDxzYYkqDwrpTFpb384Vq9ml5rL8kIy2AsiSGiqzKGLbe68bcOPaI1LXnfNol9pecF2Net0HWl9xKCkdFvWTjIweEayKoHFHp2JTziRFwPb92Q+9n8FYwuaLFlIkp3Sw+W7hseUy+fCMtgLI8NpOhGFfYfMEfB5oSPhLYBqi+4OuFe3IMcHqoVUbguKuy7ls5GDgb2KeyCc4AraBgKjnFStyTImDILpqCurpD1lK2iHtbM/t0SpRxcUNdHZSWZwYswUgLoIzbSKZfNwtGYIbCuINp0bPiJXNVt+bRvJs1lnRZ/Or5qgiGCgJmaFIaOY2pLis7EZDcw1Jtujamfc1MGfcQRGzKGR9Jzc1xe8TOV3fEGswVbEwtX1mRkxntHvtSHKvu2uGAgeSDam7VvPW3au9XAGXVmrY8WNHA/DVQAGX+Oi93LBpYtRoogLJqTVserGhg/hoogDJ/nZc7Fg2sWg0UQFm1pi0PVjQwfw38BzBji2uwr2u0AAAAAElFTkSuQmCC)
= cos A + 1
LHS = RHS
(v)
using the identity ![](data:image/png;base64,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)
LHS
![](data:image/png;base64,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)
Dividing Numerator and Denominator by sin A
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASIAAABrCAYAAADTno+mAAARxUlEQVR4Xu2dCfB+UxnHP7KmaLFE9iJZskQoFJIlS0x2IluyZ2lMthQZjBDK2Es0ITFChCQhJImIlDW7ELKF5ts8V7frXc65793vc2Ya/X/vc8/yOfd+73Oe57zvmQIvTsAJOIGaCUxRc/vevBNwAk4AFyK/CZyAE6idgAtRNVPwGWANYK9qmutsK86xo1PrQlT+xL4TuA542MSo/BbLbWE64MfAgsCqwN/Lbe7N2rvGcRJsHwWOAtYHnp6koqZc60JU/kxsBxwN3AF8Anit/CZLbeF9wN3AjMDyJrKlNmiVd41jDLO3AdsCCwALAxIiPbuLAk/FVNRUWxeicmdmPvMcjrdmFgP+VW6TldT+KWA24Fzg9Qpa7CrHUHQSoq2AJ4GrgdPtpeZCFEqwx3a6eTYDzgF+A3wQWAh4vMdM8gzdOb6V2nkuRHlupX5eo2XYY8BfgUuB1c21vqefOHKP2jm6EOW+eaq8UMtLrZlXAvT2/K3FLQbFYmS7FKClhYrc3JuBNzIdVmBUMQn9/d0pL2YFYJeAAOH0wJqA3lwqZ5l3tCxwY5VwItsaN+7ngKWBOYCZgAtSbDTmJYA5gZmBMwHZK46k//0D+BnwaESf2soxYoi5TN0jyoWtvIvmAU40j0P/fQVYHNgE+LZ5JEnr8wPfsozPRRbsWxvYGNgPSDwVidmpwGHAXamuzwWcb57NuADhesAVwPN2veraB1gLuKQ8HBPVHDJuxbd2BtYFVgQU87rNWp3VPlsNWM5iY6sAvzKOEnGJ06YRAe42cpxoEgIvdiEKBFWFmbI3v7ab++BUg3r7Xgj8CNjV/j4v8Etga/OC0v3Tw6Lgn7yk+wDZJhP9cmYgBwHHjclUzA0ouCpvKyl6eBWw3h44pQo4OdqIGbfS9pdnhChpMvlsbxP0Z1J9udj+vwR5XGkrx3HjKuJzF6IiKBZUx3eALYEPZzwfvXnluUg0vmuej0RJD5o+yy7ZprI39J2WmdDS4k+2T+NI4IVUf/WmvxV4ccgYtPSTh6UAdTqbtIFlmA4ADilo/EVXEzPuT5rQpj2ipD/JZ3oJJNnC5DN5mksCWqK+OmIAbeZY9LwMqs+FqArKAW0olnEL8ISJy6gU8uyAROYyE4lB1Z9tSy5ltRTD0LJuD+Al4AaL68jLunZAPCldn7yqLwAPZhrRElLe2BkmdgFDrNxED3/ouEOESDG7tFeoAUmIdK0EbJiYy67NHKuYOBeiKigHtKF4zQPAVYCWVqPKMiYmp9mmsEG2ekC2sTe1gsmKlyiWsYU9OAqaqsjD+grw7wGVvB04FEgvRRIzLSN3BLQ0UVyqqSV03CFCJDHR0jldQoSoCxzLnl8XorIJB9avzXR/sYyX3ryjijJqyowpcyVhGVQUI/qiZdTkPUl4koD0lBZ43QnYAdjIln7ZelT3NcD9AxrQsude86wU5K1iE2AgyjfNJACh4y5TiNrOMZZ7HnsXojzUSrhmatskqNS6hCYdx0mae6+l2WewZZwyYJ8d0hdlsvTdKcUvtIxaGTg2Y6uly0mAAthK4aeL0tnKJJ0wpH71U9klpbPVXy35mlY+EjHusoSoTo7TAPsCR7Rg97sLUYOeng0tKKwszZWZfsmLUUpe6XoFp78K7GmxCcWV0mUW4I/AMcDhgB7I79lDmV2CaXn1DkBB7KRIoJSalwg9O4TPtOaVSRy1LV97appWYsZdhhDVzVH7opSIUELioaZNTqY/LkQNmiDFM5QZ014T/cSGvt2eFO0jUgxJ33pXkQelDI42KCqbk2Rs9Hel4/UQyMvR3/VASpgUM9KSLSkSE8WZ9rdlVvJ3bXxURk5/H1aUmbveNgMqta9tAk0rMeNW/Ef7gwZlzZLPBsWIxFOZy0HB6ro5SohuBxRTzCYbmjZXEiJtU1nEv/TanKmRRyThecQ8kn/aDZWIUNpzWcduNC3lJErybm6yHb/J7mptB1CcQlkyLdXkxUig9PMX+pKnlnjK2u1uwW3toFbbEjptKUjvPdKycDfbV7S51aGtBPr2+skZ8aybaMi4tWlRsTKl3yX+2iahr69ob5R2U6c/U2BebPXLA9pkqo2O+uKmPFAFrfWZHqimcGy6ECk2qayufvVAHNVfbRNRTFNLfnnxozKRdd9fI9v3b983enq8cxUSaLoQVYii+qZciKpn7i02k4ALUY3z4kJUI3xvulEEXIhqnI62CNHXa2RUZdPfqLCxLjPNw3FSIXKeE9y8LkQTwCvh0kEPkHaRKzipLQl5ilLS+rmObOnbg6MguTKhSjoMKtrMqWC7kgjDtmFoO4cC8/qdqb7zzHMvDr2mLUJU6KBbVllZQtQyDBN3t2whmriDfa7AhajPs+9jTxOYdGnmNCcg4EI0ATy/tFMEXIhqnE4Xohrhe9ONIuBCVON0uBDVCN+bbhQBF6Iap8OFqHz4fkxycYzLZNlHISqTZ9Ss90WI/JjkqNtipHFXWdYlRF3lGXXH9UWI/JjkqNtipHFXWdb1MyBd5Rl1x/VFiATFj0mOujVGGneRpX4Y7UD7ud+qjwXvIs+ou61PQhQFZkJjPyZ5QoCpy51lcSxVUyN5uhAVO8lJbX5McnFcnWVxLFVTI3l2QYj8mOTiblRnWRxL1eQ8A3m2XYj8mOTAiQ4wc5YBkCJMnGcErLYLkR+THDHZY0ydZXEsVZPzjODZdiHyY5IjJnuMqbMsjqVqcp4RPNsuRH5McsRkjzF1lsWxVE3OM4Jn24UoSUeGHA9dxllcCequHJPsR05HPDwBps4zAFKi2oGmjTTzY5KLmxZnWRxL1eQ8I3i23SPq+zHJEVM91tRZjkUUZeA8I3B1QYhCj4cuY2lW9zHJEVM91rTvR06PBRRp4DwjgHVBiEKPh+7iMckRUz3WtO9HTo8FFGngPCOAtV2I+n5McsRUjzV1lmMRRRk4zwhcbReiiKG6qRNwAk0l4ELU1JnxfjmBHhEIEaKFgWuBd0/A5UVgaeCOCerwS52AE+gogRAhqmLoXT51tAp+3oYTqItAnuO939JXF6K6ps/bdQLdINApIerGlPgonIATyEWgKR5Rrs77RU7ACXSDQIgQebC6G3Pto3ACjSUQIkSN7bx3zAk4gW4QcCHqxjz6KJxAqwm4EJU3fY05zre8IdZWs7OtDX05DbsQlcNVpzdcBzwMrFFOE42oVaeU/hz4LbBTRT3qC9txOD8KHAWsDzw9zrjpn7sQlTND2wFH205ynSP1WjnN1F6rEhmXA98ETqyoN31hm8WpX3vcFlgAEHcJkZ7fRYGnKmJfWjMuRMWjnQ9YEDjeql4MqPoI4+JH1Ywa+8xWQrQV8CRwNXC6HZboQtSMe7NRvWjkcb6NIpS/M872/9md50KU/2bq+pWNPM63I9CdrQtRI2/lmQBlT+YHfg/8Avj3kJ7KVkFjufayVVzj1SG2WoOvZscFywW+AXgjgMD0wJqA3lQqZwGbAcsCNwZc3ySTcQz0Swyb2DLhggHcVwaWAM62gL3G9n5gXWAG4Eqbh9Axd4lt6JjH2blHNI5QyZ/rpjwAeBdwGPAA8AFgS/v3S6n2ZXuQiYpsHwRWAg4Evgjcn7KV6/814FHgTOAVQD/3qQfqjIAxrQdcATxvtmpvH2At4JKA65tgEsJAmbKNgZOBg4GXgf1SnZeI64XwCHC+8RZzxckuA6YFLgJ+aHWEjLsLbEPGGWPjQhRDq2BbvYk1ATcB+wKvW/1HArubaPzJ/pbYyhvRg5LY6uNjgXks9Zn8XW/4FYBdUn3+MrAX8DHgmRFjmdu8LXlQSdnZAtbbA6cUzKGs6kIY7GEZMgmLBHt24NPWIQnZbsB3gNmAu22+9DMvadHXv+Whive4jGJX2BY9Zy5ERRMNrG9K4AfAkrbcSTyPqYCLbam1kb15E1t5NIotvJBpQ+JwjGW3HrLPVMft5sUk5nqg5AFsPuKBUeZRHsI5GbHbADjXvLdDAsdYt9k4BjMD65iwvgfQwQUnmWekvs8BrGLejv6rJdggj/D7xn6cEHWJbdFz60JUNNHA+uTyy7WXh6KNXKNKYrtrKo2ette+Fy3vlFq/zT6QaHzOlg3XWxzp1oD4kE4H+YIt+9JtyOPa2pZ1Sru2oYxjMKsN4nFAon8asBRwl/09/bnEVx6WXhzPpQY/tcXd5KnK4xxVusS26Pl3ISqaaGB9PwHWNvGQyz+qjLNVzGZF4EMWy1BdEg4FmJdPVaw395dGBLa7ctR0MuRQBlqC6aWgOJrmJBvMl0eqZeoTtvxNz5U24ylh8HnzZIfNY9fYBt7mwWYuRMGoijNUgPNmq05vYAVIh5Vxtsqg6beztaxYPbOcUp2KbSwHaAevlhV60LRkGVS2AK7JxD8SuzmBey1jJtFLx6iKI1NOTeMYLATcAmxqAelsL5Qh+7PF7bTxLl2UPBBbLZtHfTWhq2yLmjEXoqJIRtQznb1FlSEb9t2tZJe4hEhv3GG2ivfI01E9imEkqegLU6lmdU1v5N8Bh5qnlO2u4iFKR58wZByqV8s+LUu0HT+dzYsY+kDTaSxYf0RBu7ZjGRxucbHFgWdtm4IejOQFoTjSTzPJg4SptkNo6bsDoGWaxCyblayT7aRzU9X1LkRVkc60o+XWjLbHJ9sFiZCWUNof9DfL1Gi/imJF6aIHTieSaO/L/rak0JHVO1o8Q/tekqLU/1X2wN2Xqafuo6bl1Sl+Jc8tCbZPMi0xDPRSUHxHWxX2BPRveTjJV1rUDwX5tcdLJ7ekv97ycfsysBIIEqNl7PpfpzpfN9tJOFZ5rQtRlbRTbWk/j/alaLNcWhiUydGDcCnwB7OXB6KJSttq39GpFlhV+jjZ/KjAtd7qSuknmxwVA9EeIHkz6Qcs6Y7am9fEbBgOZfP0sOlh1EbKrJhNglFCpAyfHmTtjZq0xDDQt98lgnvbfGxoy7R7rBPJuPVveTvpsqoFuLUsk0ApmXBcJgZXN9tJWVZ1ve5vxTMX8S+9VoX8f+3oodbSSt82VqBUe3skHsr2JOn8xDprK29IQqY9SOmiJZjS7wqwKq6TZHhkp/hPUvQAaq+SdkprB7U27Emk9PZPx6zkiWkvjcRHfZXH8CPbU6NNgPppkElL0UIUyiDpt3hJ5JU00PI17dGIkwLV8jj1EyHpoqWYlro6507xISUHlIFrEttJ56bM65WpVHxOKwNlYnUfaNvInXbfyrMV29YV//Z966bsvx0uWojaScF73RkCLkTtnEoXonbOm/d6CAEXonbeGi5E7Zw373XLhKhPR1DnOSlzUiHqC988bPOKhTPNS85+anKCy0u7tC+TKoCDHpZZgG0s0D0IsrYW6DeiFfxWxm9QUVZQX7Z9bMCHfeE7iO1cFuhVciJPUcZQ2z+ypc9M83D8v2t8aTYxwlIqKFuISul0SyotS4haMvxmdtOFqJnzMq5Xky7NxtXvnzuBSgm4EFWKu7DGXIgKQ+kVNYGAC1ETZiG+Dy5E8cz8igYTcCFq8OSM6JoLUTvnzXs9hIALUXm3RpnHIvddiMpkW94d0eyaa2XaByHq4rHITRGiLrKtWy56ybQPQtTFY5GL/hmQvA9fF9nmZVHUdb1k2gchKuoGCa2nimOR9cNoOhJJ32Tv03HWVbANneeu2DWCqQtRsbeTH4tcLM90bc62eLaNYepCVOzk+rHIxfJM1+Zsi2fbGKZtFiI/Frn4GzOp0dkWz9aZjmDaRiHyY5GLf0iSGp1t8WydaQDTNgqRH4scMLE5TZxtTnAjLnOmAUzbKER+LHLAxOY0cbY5wY24zJkGMG2jEPmxyAETm9PE2eYEN+IyZxrAtI1C5MciB0xsThNnmxPciMucaQDTNgpRMiw/FjlggnOaONuc4EZc5kw7kjXzY5GLfziSGp1t8WydaQTTNnlEfixyxMRGmjrbSGAB5s40AFJi0iYh8mORIyY20tTZRgILMHemAZDaKER+LHLExEaaOttIYAHmzjQAUhuFKGJYbuoEnECbCLRpadYmrt5XJ+AEIgi4EEXAclMn4ATKIeBCVA5Xr9UJOIEIAi5EEbDc1Ak4gXIIuBCVw9VrdQJOIILAfwDdJvrV77lE7AAAAABJRU5ErkJggg==)
Use the formula cotθ = cosθ / sinθ
![](data:image/png;base64,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)
Using the identity ![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
Use the formula a2 - b2 = (a - b) ( a + b )
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
= cot A + cosec A
= RHS
(vi)![](data:image/png;base64,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)
Dividing numerator and denominator of LHS by cos A
![](data:image/png;base64,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)
As cosθ = 1/secθ and tanθ = sinθ /cosθ
![](data:image/png;base64,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)
Rationalize the square root to get,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZ4AAABJCAYAAAANMEAsAAAalElEQVR4Xu3dCdR931gH8C8RokRCEWVIigYiU6ZlJlOUuSLztDJkmSpDmTOTzBKVIUMyK0OGipWpzFPImGSKQuvjvzfHXffcc+69533fc++791q/9fq7++yzz/c853n28zzf/ewTpbWGQEOgIdAQaAgcIgInOsR7tVs1BBoCDYGGQEMg+2R47pvkF5L8Y3uvDYGGQEOgITA5AveaasR9Mjx/meTPk7xgKnDaOA2BhkBDoCEwPQL7ZHjemOQ3krx7epjaiA2BhkBDoCEwFQL7ZHj+I8lZkvzvVOC0cRoCDYGGQENgegT2xfCcIclbk5xxTYh+JslvJrlrkv9b89rW/fgh8KNJ7phErPu/Z/L4TYZn8iJ2ZBqzkOF9MTwXTPKgJJdY4+X/UpI7Jblpkv9a47rW9Xgj8PNJfi/JjWcgN02Gj7csbvr0Ry7D+2J4rp3kskluNvJN/EQhIvxqEiG6XW6e+wplJb7LzzGHuY/F8leS/FaSXz/C0G6T4TlIzPzmsBMyvC+G5+7l/f/hCDn43iTPS/KkJM8e0X/OXU6V5PVJPl6Mzxznepokn5vjxBbmtA6WvpsnJ/m3JA84gmdrMny4oDcZnhjvfTE8f5bkpUmePgKfX0vyOyUs97UR/efc5beTPDTJvya5SJKvbzlZCu1uSR6Y5MtbjuXyayV5RJLzJPnPCcY7yCHWxfInk7wyyS8n+dBBTmzJ2E2G+wFvMjxeHxyZDO+L4XlNkjsk+ecBBUAoX5fk0UmeesjKYurbCbWcK8mjysA/O4Gx+KFC0rhQko9OMGELAcLNKM6ZvLEpls9J8r4kd5kAq7FDNBlejVST4RPwGasPjkKG96ZywYfLqvoLA18vBfi3STCBPjb2S59hvxMnuV6SvyqG9OxJzp3kU1vO1Uf7jiTIGv++5VgnLwsBXsHttxzrIC/fBks5nj8qFTP6WG5kjvf4LyMe4mRJrp7kuStyR02Ghw1Pk+Hx+mCMDI8Q3fW67IPH84Ml1OHvUBNCulgJj2wblhq610H+Tvl8Msn7k7wkyeWTnLOsvre575SGhzdGAVwzyQu3mdQBX7sNlmctYU5kg1f1zPOWSeQgr5bkzSuehdH50/IeJYi/1NO3yfDhGZ4mwwf08e2D4UENRBQ43wBGVrZ/l+RdSW6+Bp4U+uWSSD6/Osmbknyz5/ofSXKZspH1tUn86+tLyVMw50jyliQvGxmO+r4kV0zCRdaUCeL9oNZuW6duW8NztiQ3LPOC2/WTPLyQC4TuJOS/sYAdGfzFJJcsyXoe6WKfesmlknjfyiMhVGj2JVw1yfeXnAssx7ZtsWQsGJO/SKJW4LLm+dD2eX19xucUSR6X5KeTXGmF59pkePjNNhleTx+MkeFh1NfssQ+Gx8d8nSTXHXj2H0jy9iQPKQnvIah85DaWfqKQFhARzlsU39MWLrZxFbvpM2V8FO1LlxDMgxf6Unb3THLqJPdP8pEkFPaNyn//z8DEhGJekeSLpZ8x5BiuXMKIQ8+16vdtP1r5nPoeUNV5odXYSMAv5tXOXMgRwnEWD2cqxphBfluS+3Qmy/jLE8H2r4uhYqyEsRBLfEB/kwTR5PEjQZgCSx7nV4tR6but78w7us0S48PoPKEYHbR4nmxfazI8/GKbDK+vD8bI8DDya/TYB8ODVIDuSJmvapSa0BQFLzcy1BgzYTnKorZblP0yF+hsHpRbeXGSRxajU/vC1mrfarey5yhinso/FfZYXdkzTlbEVvPvXDExJYEkwnletd26EAxshKXAtmnbfrT13idJ8oZCVMAWW9YYHQZH6OiJnQ5wf2apu1cNvEXA7QqejPx7Co6/n0R+rzb/TXl7b0Oh1KmwRMk3p4uv8NTMrxof7/kqxVNax+gYo8nwsHQ3GT6BcLSOPhgrw8Poj+yxD4aHsqXIhSpWNatxBUSvUfbxDEH0opKj6DKWGBLleYSQKLZTlnAaw6JqgpVvbRQrJXPn8n98T1nxO7pBWKx6LJS0e6kxhybbR2P2riQCGc1uKApl+VnF8PaFe4aetf4+1UfLg+NdKkdkbovtpCWBbsEgfNatryds5hmxchiYqnB5kLwZfxmsZR7eUwrTb8jwTIklo2muFx4RKnVf+R55H+/NokZ4bcjTqfg1GR6W5CbD6+uDdWR4+A2M6LEPhuflSe63Irm76UdLYQrjCd9YvbuPenDdnA0DhDIsZyQxzLicviT7KSNhsMo0EyoSElLr649HvJvFLgyb/Mki20yC2y563oHq3KvaD5dSLxhny5ow4K1KqOrzPX2Euxj7VSEhBlLozP6dDy4Zh6LlJVbcul0Yd3tjGOdqkGCqwZJx5RUx4F0WI2Mm/ybPxTNd1abAso6/7kdbjY8wIqbbWKPjfusanibDy6WgyfB347KuDG+gvr77kn0wPO8t8f4henQNU9ykJOSHwKPQJe4v2uloRa0sT1WIzy/JYJsk0Wl5McJ5FOBiKR7urBBLdyU/NIf6u5AM2u6ymnI8MCtoXpPx52B45HVQ1vv27/RhUY0H/DzTYmPYhRk/XTzX7u88B8QCuSVY9LWpsKzjC516B0Ohttpf2FBIUL03eSxEkUqUGJKHJsPJYS2emgwPSeMWv++64bFCt/LGaBpqNTFrp//Dhjp3fhe/t6FSrkJ4h3Kn2ITIlKtBEsCo66O/GqoyR/zv8y+E5MZM5QYlpNfNZ9TrhPR4FVb6PIU+RtiY+0wRpuBNmQsG4bL9O35nIIQqsdm64ckaopOHq6y97rwx2LASjUsxdNsflHeEALKqRM/UWPKELTiEcIea700uklFVX9BfXiE6PBLLUGsyPIRQ0mR4fX2wjgwPv4ERPXbd8Ejs8zqEIIZapaJS0nIPfQ0BQCjHSabdlaiVssoIPA+ekPGsvoXehG6W0aYrvgwPZYvBJrSyrNW+i+NY5cp7PLbnOvOVTxF2YgCHWHGrcJrio/UurOTt30GN1tDMGVxhSzj6XZkfocxuw4gTxqshOkYC0aASBeyXsblykYRhTF6SkKjwHc/JWIvsw6mxrO+VPJCLVa2G2JBBuuQCc0Sp5/kMGZ8mw0Nf+TSGp8nwMM5b9dh1w0OJ37Z4ImOAGLP57jFlJcr42C9SG+/KKl7+otbmksORHBeOWywJA1tKEFVRf+ElK1a5nsWmrxCelccHOj9WJhSj05dzqd7UaSeoiTaF4RHqEpL8qU51CDkXWPJEarhMSLKbk2IsGPvTlUS9fvATxqxN/gfVmqfUJWFI7PM+hfYYH5UXeFZKKdV2EFhiGNok653+wwoBXMZoq90ZzWp8xuR7mgyv/tKbDJ+wt2ysPhgrw2P06+g+u254JMKtFlGqxzQhM8pd/oH3sazduyh5Cq/mcqw0sdt4FbU2mmuFuexYx1Cyiq+N8hSaY3RqqRSrdPtPGKpuUcllfes4xvjxJPdY8XCVukwZE6JtClZO8dHaQItoIZclBMVQwA+xojahNO9OXgQjUP0xBAmEAs+LuYaZRj5twtXqc6qNtrhnyz2RGYTZGCSLEfT2LlvuILC0CCEvvLnKUlx8VdXooIPbN7Rsk+86xqfJ8MEbnibDY7TpFn123fDwTpSmp2TGtFpgUTiHclzWKAEKxYqbYanMKZTtqgS71zF8VvSqL/N6kAzkLTCKFpUR44AJ99micJEFKMduXxUS5DAoYeEXJAXGzmq/mw+R16LMGBtjWuE/o1CQbaAcm7DuPssUhofngrHlr5yUkJoNr93GENlnADtEATjAQJiRF4koInfnPdWcVa0cwQhjxHWbewl1faV4VUJfGHAHjaWwn5yTit59TR5HXqfP6NTryB2GpLDkqpI5TYYP3vA0GR6jTbfos+uGR5KfAZHnGdvkHuylEB7bJh8y9n671G8Kw7NLz7vNXOUBeLQIHasYlcJ/FiBdj7jvvsK5QpVK8HS9tcX+TYb731yT4fFSPVaGx484sueuGx67/H2oVp1jW928aJOiDYmtfQeBqUvK7yu2vht7HxiTdRiSU+HRZHi14bHfbqqjPaZ6Z3Mb50hleJcNj5CDkJUk2qrV4bIXLo8gtKNSwLINjnMTksOaD0ztLxG2muIguMOa92HfB7tOOFZeal3Zm2quTYaXI9lkeJyEHakM77LhcQYNlpmaW5s0yX65CNUAlm3M3GTMds3+I0Bu5JmQFY5abpoM77+8HcQTHrkM77LhwXyyaRAzatMmxomyi7E25xMyN32+dt20CNjA6th0C5a+g9+mvePwaE2GhzFqPb6DwCxkeJcND1aU/Rr+ttYQaAg0BBoCO4LALhseSV0FM52v01pDoCHQEGgI7AgCYwyP4ot2ZY85Wrrvse2vsIfFno6pms2YaKfd6gJTjd3GaQg0BBoCDYEDQmCM4TmgW289rIoAysz0HfesAnBrDYGGQEOgIbA5Avfa/NL+K3fV8KgqoO7Xj62oYdYMz0FITBuzIdAQOE4INMPTedsMDk9HeZHWGgINgYZAQ2CHENhVj0eZEqd4XmCHsG5TbQg0BBoCDYFS/XcIiDmSC5TTv1LZPT40//Z7Q6Ah0BBoCMwIgV31eO5XCnweSPxxRu+nTaUh0BBoCOwdArtqeFConWbZinzunUi2B2oINAT2HYFdNTzOxvndUqtt23fkUDhHYd+1lc3ZFsq9vl6pkTsm4WXPpVzOXgPeHm5/EZib4XEeiSOT3zIAuUPXnHD50S1fjcPW7lTK7hx1wcctH6VdfggIKK6oeveNZ1Ag9BAet92iIXAwCMzJ8DA6zsh5Y5L7rnjc05dTR50ds01zcqeTKp3n45TP1hoCYxBQTt5xCI5FOKojEeo8m7c+5o21PhWB2XjtczE81eg4ztmpoJdfISu8FKeO/twW8uTMjucleVKSZ28xTrv0+CHgm3lyWfw84Agfv3nrRwj+Dt96Fl77HAxPNTreJZr0e5P8cJKv97zc6yXx7ypbvHwHwClvf4kkX9tinLlcetkkVyg5iLnMadfmsQ6GjiJ4ZTn2+kNH8KD75K2vg/sRQL1TtxyL5ZF77XMwPE5SVN7m1uXUy9cnuW2SN/e8cmfwnDLJnTcUCd7O65I8OslTNxxjTpedKgnMPl6Mz5zmdppS2mhOc1o2l00wfE6S95WznA7z+fbJW98E98PE2r32UYaP3Gufg+FZFCThi08keWiPhKFQO3lUmGyTdpEkf5tEfPxjmwwws2uchAkrlb89W5+neNjTvlaSRyQ5TxJkkDm3TTCU43FE+C8cMsttn7z1TXBfJUeM8t2SPHCio9v3WYaP1Gufo+HhBqI3S/ova45oQGl92YaajFBerIRJ5qKkN3yUCLmcK8mjygCYfl/edLCJr3t6EsLNGM75dNdNMTxrMfbk9VUTY9c33D5565vivgpqhKO3JrnQBIxX99l3GT4qrz1zNDynLiEMeZ5ljTd0qZLcXfd7P3Hxlt5Vjrxe9/o59fcscl2YgEKHZ09y7iSfmsEkT57kn0se5PYzmE/fFLbB8GQlHOxMqD4WJqNrIeAIj6FmvKsnee4Ktty+eOvb4D5keN5RTiZ2SOQ27TjI8FF57bM0PISF8HBzGYhucxgdgbKy2YQU8ANJ3l5OLRUG2uVGCX0yyfuTvKQwAc9ZjPZRPxcvzDu8ZpIXHvVkVtx/Wwzh/tUkV+u5xy2T3L383pezdCmjg6np/UkQf6lnvH3x1rfFve+V0gtTGZ7jIMNH4bV/693N0eMxr0cmeVuSxy9I2PnK3hsr+03amYqivlHxFMaOQSFcLolk6KuTvCnJN3sudlTDZZKcJclry7++vj4UiuYcZdOs8OGYsBQm4BWTcJU1+5F4Pyi2fQfjjX3WTfudLckNy8Xwun6ShxdygY2+KMjfWBic/DmZ9pLFg5V7W+xTL+HlooIql4RIodmXcNUkaPhYZkMbj7u3nwJDVPwzJrl4z7w9nw3KvD7GaZnxOUWSxyVRjFfh2z6PdVNv/TjJ7raG57jJ8BivfVN9sPK6uRoeSsteHgai265dTh2lrDdpcg7vTnKNso9naAwfu1I6wnvivbys8xYF+LSFiykgxIjPFI/KptRLl+Tzgxf6Unr3TCKseP8kH0lC6D2v/7aXaVUTknlFki+WTq65S5IrF+LE0HMdxO+wvW4ZWH6Od1qNDcrxIoPwzIUUwWAgilgUeK/+WXTcpzNJRp9Bhqkjzxkq/4SxXlo8hlq7b3Gx0vesU2D4xFJB48IrFgy+Me/mNkuMD6PzhGJ00OF5sH1tXW/9OMrutobnOMrwkNd+ELpith6PlSwSgQRkt2Gs+P9uuiEa6xqe6xQiAqVR2y3KfhlnAdUyOzywFxdP7SGdvpSOVb9Vbw0NUsg8FfXmPE9d4TNOVsZW9e9c8Xw8KRjwvGpDRUcwgAtFdpTtJEneUJK8WEvLGqPD4AgdUd61wfuZZT9XNewU6O0Kjoz7ewp+KPgf7lzrvylvxJEh0shUGI4xPKZYjY/3a/8Zz2cdo2OMdb314yi72xqeKk7HSYaHvPYD0SVz9Xg8LC+AEvG3Nh86hf0nG6JRP96blPDU0DAvKjFjK9baGJIzlFASBWdPkZAaw2JDqph/bRQsZVP3HDmy28ofBVdYrHosBN29lGBBl+1jpnlfEoIIBd2QlHzYs4oXtarc0NDzTvE7z00eDTPRnBbbSUsC3f4I4bNu2RlhM8+GncfAVIXLc0Sj95fBWubZPaUw/IYMz5QYWkCQhb5QW/fZ3Ve+R97H+7KYEV4b8nTqGOsumo6j7E5leI6TDI9dPE2hG749xpwND0UijGIFXNvfJ+EZCKts0mq4wr6Xh40YgOIUm3c/q/iXl5V8N2cjLCgMd/OSIGZc1JMTKqRAhcFq3F7IyDOpcuwE1XUbwyaPssjYkSRUP4yXoPrDqubYcH3Mc5OGrqrcUF9jGIXO7N/54JJOFC3vsOLV7cKoO12WUa4GCZYaDBlVK3mG+wudCxkzeTf5LR7pqjYFhnV88mDxIHQ7plXjI4yI6TbW6Bh7XcOzj7KL6apAK8bZsiaEfauSG/58Tx8hW1GBVWHN4yTDzfAsCIqVobATBVUbhWvfxBh66jK5qwlaCtGKfKhR6BL3F+10ZBBv1lGMzy9JYSw55fIpIkwzinCx+Ci3Vqilu6IfmkP9XWjGhsVlVbStuuFllTtUSuigDY+8js25fft3+jCoxgNunmWxMZTCi59eouh5DogFcksw6GtTYWh8iVn3JB/ey5hG/oQEVbiWx0IQqUSJoevX9db3UXYPy/AcFxkmc+t47UMyOvr3OXs86IyUlGS+ZjXz2SRYY9scYbAJJVVuwaY0OQthHsqdghMiU64GSQDjro8GWxVVZTWdfyEkN+aF3aCE9Lp5jXqdkB5jasXPY+hjho25zzZ9rETNQWWJZft3/E5ZC1Fis3XDkjW8gWBR2Xrducj7odcbl2LoNmWUvBuy8rkVDzAlhvJsqLu8WPnIoeZbQyhhVJFk/OUV8oyRV4baut56He84ye4UobbjJMNkZF2vfUhOR/0+Z8PjASgRIQarXB+pEA/q8TaNAQG2VXk3f9QdEwFASOcFCytSK2YbI61wrXStYK3Chd6EcJbRpivGdYXsnkIsy1rtuziO1a78x2N7rjNfeRXhJwZwiBW3DX6rrvWurOTt30GN1iwUGFrhSvj5XXmfxb0vGHFCIDVEx0gIs1aiAE/X5spF8oUxeUlCobxjnpOxFlmHU2MoHHPv8mw1V9eHTQ2xIYF0yQXmSJ55PkPGZ6y3fpxldwrDc5xkeBOvfRLdMXfDY+UrGc8AUFQqSqPRbtNq2RFKzqa9Ze0xZUXK+Ng3Uhuvy2qe0qlVieVwJMmF4xb34MCXMkRZ1J8HZ+VqlbzY9BXCYxQ/0PmxMqIYnb64deXjn/aIa6MJdQlFOsyv1sGTc4GhRUQNlwlFdnNRjIV3fLokqMn6wa27yVf+B9Wap9QlX+jP6xTaY3wuWHIArzlgDBlBHhhm4qq2jNFW+zOa1fiMyfeM8daPs+xOYXiOkwyv67Vvo3e/69q5Gx5JeCvVO5R/VvNWwts2K3IMI8ZimXdgJUvJU3w1yW3Fid3Gq6i10cxDmEutLkwlq/naKFHhH0an5qSs1u1DYai65fSX9a3jGEMF73useOhK/6SUCdNRlOo3PRtnGXM5LF4AQwE3hIrahNIkgDHBMAEtBBAjEAo8J+YaZhrZxBbU6vOpBl33CtXx3BOZQZiNQVLZ3AbkLltuagytir1XYc1VhWar0UEHt29o2ebedYzPGG/9OMvuFIbnuMiw72cdr31bnbtThocidXwBpYRCbaX8oAkQqJRe1F003cVGGXgpVt4MS2VQoXJXZdi9RrjEyl4VZl4PkoH8BWbRYhjGM2HCyVdRvPJVlGS3rwoJchmeWxgGSYGxs+rv5kXs2KfUGBtjik8/o1CRbaQcm7ieANJvDQFXjC1/5aKE1Gx07TaGyH4jmAmhen7PLrzIe6TIMY54pDVXVStGML4Ycd3mXkKfXylelRAoBtxBYciYYAJZZAwxI+Vx5HX6jE59DvKGGSksuapkzhhv/TjL7hSG5zjIcJW7sV77VPrh2+PM3eMxUUqc1wMk4SZ/p2hW1xSefTPLaL9T3KONsX8IyDVZlPDSho6+Fv6z8Oh6wn2ICOMK8yg6umrcIW99/xAf/0RTGJ7xd9vtnmO99gN5yl0wPOqX8XLUs5JzmbIWmdCXFbq9Mdsw5Q7k5bRBZ4cAeeF1Cd0dlbwMeeuzA+0QJzT1sQiHOPVDvdU6XvuBTGwXDI8PXYjB7n+l/6cOH7H8EtnyN2MKdB7Ii2iDzh4BdG7kFgsVXvhRtuatL0efnrBHSuh1LudSHaWc9N17Ha/9QOa/C4ZHIp4wMTpqbLXWEGgInEArb956k4R1EZiD1z7bIqFdMDGaUHHtUxEzb60h0BA4AYHmrTdJWAeB2Xjtu+DxANY+DWe6IAK01hBoCDQEGgI7jMCuGJ77FaaPkFtrDYGGQEOgIbDDCOyK4dlhiNvUGwINgYZAQ6CLQDM8TR4aAg2BhkBD4FARaIbnUOFuN2sINAQaAg2BZniaDDQEGgINgYbAoSLQDM+hwt1u1hBoCDQEGgL/DwTvEdGF0a1uAAAAAElFTkSuQmCC)
Use the formula a2 - b2 = (a - b) ( a + b ) to get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Use the identity sec2θ = 1 + tan2θ to get,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMAAAAA3CAYAAABaS0WmAAAI10lEQVR4Xu2dd8x0RRWHH+zYC9ijiF2EYC9YCXYsqBG7iL3/IcZoFGuMGtQoRhPFLhp7sCuWKJaoYECwxKhg713sLQ85k1yvuzv7fXfu7t13zyRfvrx7556d+c35nTZz7+5BtkRgixHYY4vnnlNPBEgCpBJsNQJJgDbLfzvgjsCT24jbaikrxTIJMFzXLgx8AfhJkGC4xPYSLgH8tr3Y5hJXjmUSYPgaPhx4GfAN4ObAvwaKPB/wdODFwJ8HyvL2ewOvAK4L/KaBvDFFtMayOtYkQBWihR2uAlwTeGX0OqCB0l4KOA24KfCjYcM75+63AtcIcv6zgbyxRIyBZXWsSYAqRHM7nAu4P/BO4HPAVYFrA7/YfZHn3CkBzgBuDPxwoKwLACcDnwSeNFDWmLePhWV1zEmAKkRzOxju/Bz4LvBR4A7A1YHv7L7I5gTQO0mmewIfGDiuMW8fC8vqmDeFACrW7QGTpM8AXwL+M2d2lwMOAa4EnBT/5vXV2lp1uBrwVeDjwDJhwgWBOwHviTEcH97gJsCXq6gv7jDUA+wLPCi+QtweALw8kmBDqjcA/+4NQT24IXAb4JvAh2f0KbfcFjgQeEck/n5+eeBuwEXC24jlsm1MLKtjmDoBdI1PA34Wsezfgf1jAd7cm91lgRcBvwJeAvwUOBi4HnBMr6+gPxO4GPBC4AeAivPg+PuvFeTuAXwC+FP0U8ZTgbuE8lSBX9BhKAGM9+8X8u8FXLyj9GcBb+p99xUjiTdMej1whTAKGoavAc/r9NcIaSDE9n1BGEljsv4x4PzAB4G3AK9dEoQxsawOYeoEuC9wC+DxnZk8OurtNwJ+F58be38EODaUv3R3flq/owDJY1MhtNxfiWpLsYaSxDhZ6/b1BcjpWUzY9ESlPS4S4UcAx1VRX9xhKAGK9PMAX4yE2urKrKbyq/hWnF7X6SDubwceAhRDozF6YuCpsfl24Pgs4Pude/3bPRHXrVYRGxvL6lJMnQAfihhW61qaCn2ZcO0CfKEIc1TwWwN/6/R1gVXqp8Rn5w4LqFcwXCkWXGXxu/4B3GdBJUe8Do/EtxtGWGp8V3iV51dRXw0B9GinA0fE2Prfel7gvYB7BIY1zr00wxmTe6taKrpNz6BH1br7v8SZ5fHeGJWxGgFWgWV1KaZOAJXq7uFWtWYnhkXrxvTGuJb6HgW8BlDJLx1JqQtoeFIqM7pwXbU7ti+tovP/HSSY8XW/OnNl4KFhLbWai9rewJGAFZpZzfDssRFC/H5OH8MQPY1J+LwmUQ1prP+fOaOTVlqvWXDrdtHI3DKMRCGGmNrEUpLrJTQkf+zcKKnMz8yD9NSLWgssd2MJ//eWqRNAxTLBPKgzbC3MIzsW6wTgzrHZ84ew6lZmXAhj1W57N3Boz7ItC+KewAs6YVf3Pj3SY8KLKH9RWxUBTHb3W1D/n4dFUWLxc079poEx/PslcFjv4nWimGDuoUed11phuezaze03dQKUgRtzujFkLKvbVckE2NDFYwgms9cHzl6AiAnaKXH9Br1QaRkgHxihVjfeLfcZamlltXxazn6VZRn5pU+LHEDv4lg+Paf+73UrNYaQVn+6YWMJnSwIlCpXd/xWfL4VciVZtz071shCxaKjF6vCsor7VAlgoqqLfX+n1OZktBxu7GiJ9QwmZlojQyJd6qxyZ5mjBHDRrfjo/me10rcvx/jXuPjVc+5zvMbbhgMSsVZFWrQwLQhgJcgKjvV/S5o2y8MS3yqNOHrd4xuGmN1mBcnwqoROKqsJcUlo7xq5Q79YoEy9hqGqYZWeRFn9at0qsdxYArwq3K8ksN5cmvGxVs341pKezRjfJM4wqV/DV6FdDDeq7K/bv2jsKfTBsa+hlXnG9zoX/dwkXOWfF5MX73LJBmduWhDAEMRQ8VrAj2MuxuRiqWUuYYyhYjdnUWk1OnsBN4t+4udZotLMDyyR6jm6Z5Xsrzd2U0sSuJOtp/nsGrHcWAI8N5RN4EsSprVXEbWy5eyNEzT8+FQc+tKqleYiGjKp/KfGh1ot69cSphDIS7P6FjnK2Ad4xgI0S8lRpbBE2pVdXYRehxYEcCPQgoBFACtdKqz4WQAozRDHZPtWUSL2EJ6JvNUx52ulx0qOBsANRVuZp7vdZa+hyPM7TboNfyTGE6Is3a0urRrLKvZTDYF0p1p5LZUKXioN1u7LYnQn506uFs7TjnoBk2HjWqtIpdRZ+qukVo5+HQvvXoKL1O3rjrPlU5XBHV+TaUmn9evGy+58WhtX6ZWpxXtblA7dCPKI9K62FgTQkruB5f/mLIY6btx1m4Rw30LsTGjFQQwM//Sqeg6rTIZDJacpO/EaAytI3eZ3GZr+JbyMIaoVo3ViWcV+qgSoDnwHd2hBgB0MT9upJQHa4tlCWuvj0C3GtGNlJAGmt7TG4kdHONHigZjpzXBCI0oCTGgxciirRyAJsHrM8xsnhMAyBHB7+/NxinJ3h25lwOqL1YhsicBkEFiGAKsYrEdosyUCu4LAc3al87y+SYAWKKaMdSCwowiwDgDzOxOBfDVi6sB2I7BMCJRJ8HbryI6e/TIE2NEA5OS2G4EkwHav/9bPPgkwbRXw4RqfXfbRw014ue200ZwxuiTAtJbMI8oPizfMmXtJANfIp7M8vp2tMQJJgMaADhQnAXxCy5d7+ainz9z6hFUSYCCwU98IG2l6Gy/Wh9KTACMuY3qAEcFtIDoJ0ADERSKSACMDPFB8EmAggLXbkwA1hNZ7PQkwMv5JgJEBHig+CTAQwNrtSYAaQuu9ngQYGf8kwMgADxSfBBgIYO32JEANofVeTwKMjH8SYGSAB4pPAgwEsHZ7EqCG0HqvJwFGxj8JMDLAA8UnAQYCWLs9CVBDaL3XJYBvvfaHLvIw3AhrkQQYAdSBIv2NMn/0z9e4ezDOVyX6e13+fKkvCfbV8b5mJlsDBJIADUBMEZuLQBJgc9cuR94AgSRAAxBTxOYikATY3LXLkTdAIAnQAMQUsbkIJAE2d+1y5A0Q+C9CcdxHQzba0QAAAABJRU5ErkJggg==)
= sec A + tan A
= RHS
(vii)
To Prove:
![](data:image/png;base64,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)
Proof:
LHS
![](data:image/png;base64,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)
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)
Since ![](data:image/png;base64,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)
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)
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)
![](data:image/png;base64,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)
As tanθ = sinθ/cosθ
= tanθ
= R.H.S
Hence, Proved.
(viii)
To Prove:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Proof:
LHS = (sin A + cosec A)2 + (cos A + sec A)2
Use the formula (a+b)2 = a2 + b2 + 2ab to get,
= (sin2A + cosec2A + 2sin A cosec A) + (cos2A + sec2A + 2 cos A sec A)
Since sinθ=1/cosecθ and cosθ = 1/secθ
![](data:image/png;base64,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)
= sin2A + cosec2A + 2 + cos2A + sec2A + 2
=(sin2A + cos2A)+cosec2A+sec2A+2+2
Use the identities sin2A + cos2A = 1, sec2A = 1 + tan2A and cosec2A = 1 + cot2A to get
= 1+ 1 + tan2A + 1 + cot2A + 2 + 2
= 1 + 2 + 2 + 2 + tan2A + cot2A
= 7 + tan2A + cot2A
= RHS
(ix)
To Prove:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
[Hint: Simplify LHS and RHS separately]
Proof:
LHS = (cosec A – sin A) (sec A – cos A)
Use the formula sinθ = 1/cosecθ and cosθ = 1/secθ
![](data:image/png;base64,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)
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)
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)
= cos A sin A
RHS
![](data:image/png;base64,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)
use the formula tanθ=sinθ/cosθ and cotθ=cosθ/sinθ
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Use the identity sin2A + cos2A = 1
![](data:image/png;base64,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)
= cos A sin A
LHS = RHS
(x)
To Prove:
![](data:image/png;base64,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)
Proof:
Taking left most term
Since, cot A is the reciprocal of tan A, we have
![](data:image/png;base64,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)
= right most part
Taking middle part:
![](data:image/png;base64,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)
= right most part
Hence, Proved.
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A
Answer:
sin A can be expressed in terms of cot A as:
And we know that: cosec2 A - cot2 A = 1, cosec2A=1+cot2A , so cosec A=√(1+cot2A)
Therefore,
Now,
Sec A can be expressed in terms of cot A as:
We know that: sec2 A - tan2 A = 1, sec A = √(1 + tan2 A)
And also, tan A = 1/ cot A
Therefore,
tanA can be expressed in terms of cotA as:
tanA =
Question 2.
Write all the other trigonometric ratios of ∠A in terms of sec A.
Answer:
SinA can be expressed in terms of sec A as:
sinA = √sin2A
sin A = √(1 -cos2A)
Now,
cos A can be expressed in terms of secA as:
cosA =
tanA can be expressed in the form of sec A as:
As, 1 + tan2A = sec2A
⇒ tan A =± √(sec2A -1)
As A is acute angle,
And tan A is positive when A is acute,
So,
tan A = √(sec2A -1)
cosec A can be expressed in the form of sec A as:
cosec A =
cot A can be expressed in terms of sec A as:
cot A =
as, 1 + tan2A = sec2A
=
Question 3.
Evaluate:
(i)
(ii) Sin 25° Cos 65° + Cos 25° Sin 65°
Answer:
(i)
(ii) sin 25°cos 65°+ cos 25°sin 65°
= sin 25° cos (90°-25°) + cos 25°sin 65°
= sin 25°sin 25° + cos 25°sin 65°
= sin2 25° + cos 25° sin (90°-25°)
= sin2 25° + cos2 25°
=1
Question 4.
Choose the correct option. Justify your choice.
A. 1
B. 9
C. 8
D. 0
Answer:
Following is the explanation:
9 sec2 A – 9 tan2 A
= 9 (sec2 A – tan2 A)
= 9 x 1
= 9
Question 5.
Choose the correct option. Justify your choice.
A. 0
B. 1
C. 2
D. –1
Answer:
Consider ( 1 + tanθ + secθ)(1 + cotθ - cosecθ) ,
=
=
Multiplying both terms, we get
= 2
Therefore, ( 1 + tanθ + secθ)(1 + cotθ - cosecθ) = 2
Question 6.
Choose the correct option. Justify your choice.
(Sec A + tan A) (1 – sin A) =
A. sec A
B. sin A
C. cosec A
D. Cos A
Answer:
=
=
= (1 – sin2A)/cosA
= cos2A/cosA
= cos A
Question 7.
Choose the correct option. Justify your choice.
A.
B. -1
C.
D.
Answer:
We know,
1 + tan2θ = sec2θ
and
1 + cot2θ = cosec2θ
Therefore,
⇒
Therefore, option (D) is correct
Question 8.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
(i)
(ii)
(iii)
(iv)
(v) using the identity
(vi)
(vii)
(viii)
(ix)
[Hint: Simplify LHS and RHS separately]
(x)
Answer:
(i)
To Prove:
Proof:
=
=
Since,
=
= RHS
Hence, proved
(ii)
To Prove:
Proof:
LHS = +
Use the identity sin2θ + cos2θ = 1
=
=
=
=
= 2 sec A
= RHS
(iii)
[Hint: Write the expression in terms of sin θ and Cos θ]
=
Use the formula a3 - b3 = (a2 + b2 + ab)(a - b)
Cancelling (sin θ - cos θ) from numerator and denominator
As cosθ = 1/secθ and sinθ = 1/cosecθ
= 1 + sec θ cosec θ
= RHS
(iv)
[Hint: Simplify LHS and RHS separately]
LHS
use the formula secA = 1/cosA
= cos A + 1
RHS
Use the identity sin2θ + cos2θ = 1
Use the formula a2 - b2 = (a - b) ( a + b )
= cos A + 1
LHS = RHS
(v)using the identity
LHS
Dividing Numerator and Denominator by sin A
Use the formula cotθ = cosθ / sinθ
Using the identity
Use the formula a2 - b2 = (a - b) ( a + b )
= cot A + cosec A
= RHS
(vi)
Dividing numerator and denominator of LHS by cos A
As cosθ = 1/secθ and tanθ = sinθ /cosθ
Rationalize the square root to get,
Use the formula a2 - b2 = (a - b) ( a + b ) to get,
Use the identity sec2θ = 1 + tan2θ to get,
= sec A + tan A
= RHS
(vii)
To Prove:
Proof:
LHS
Since
As tanθ = sinθ/cosθ
= tanθ
= R.H.S
Hence, Proved.
(viii)
To Prove:
Proof:
LHS = (sin A + cosec A)2 + (cos A + sec A)2
Use the formula (a+b)2 = a2 + b2 + 2ab to get,
= (sin2A + cosec2A + 2sin A cosec A) + (cos2A + sec2A + 2 cos A sec A)
Since sinθ=1/cosecθ and cosθ = 1/secθ
= sin2A + cosec2A + 2 + cos2A + sec2A + 2
=(sin2A + cos2A)+cosec2A+sec2A+2+2
Use the identities sin2A + cos2A = 1, sec2A = 1 + tan2A and cosec2A = 1 + cot2A to get
= 1+ 1 + tan2A + 1 + cot2A + 2 + 2
= 1 + 2 + 2 + 2 + tan2A + cot2A
= 7 + tan2A + cot2A
= RHS
(ix)
To Prove:
[Hint: Simplify LHS and RHS separately]
Proof:
LHS = (cosec A – sin A) (sec A – cos A)
Use the formula sinθ = 1/cosecθ and cosθ = 1/secθ
= cos A sin A
RHS
use the formula tanθ=sinθ/cosθ and cotθ=cosθ/sinθ
Use the identity sin2A + cos2A = 1
= cos A sin A
LHS = RHS
(x)
To Prove:
Proof:
Taking left most term
Since, cot A is the reciprocal of tan A, we have
= right most part
Taking middle part:
= right most part
Hence, Proved.
Testing
Question 1.Draw the graph of 2x – 3y = 4. From the graph, find whether x = -1, y = -2 is a solution or not. (Final)
Answer:Given equation, 2x – 3y = 4
⇒ 3y = 2x-4
![](data:image/png;base64,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)
When x=-4, then,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
⇒ y = -4
When x=-1, then,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFsAAAAqCAMAAADrltfPAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjqQOmY6OmaQOma2OpCQOpDbZgAAZgA6ZjoAZjpmZmYAZmZmZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAttv/tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///brxUD+wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABgklEQVRYR+2WbU+DMBDHe+hWH4ag86Fz0llHC/3+X9BrgUXjKG2hMTFeQsKL8uvd/x44Qv666eMDwGXlF6bIPA92OA7PpCkv3n3gigay10gV8OLBbsunMLZlSmRzgFUtwHELL2QEmxtNOH6o2XgA8qaOYCtqiJqh38WoNu19RcLZmnVERW/zAY0K9dbLYA8hW/hk5uSgZiadxlwlJoe7gth8XXfodvs4UYuhmogVoiUGrHdVWw4hnJc9kK2usNU0L+yDxTiezAnRznjTJ63QDDL0G1xw1DyiwD268v/IbynAzFRTNElezeCx/Z8iOGHaV3xtsx/jJ/paMzexi6e+P4077xc7jddEGl1SGIrCv83D5TQhbXm3RcnTGHfPtFmXSr+lI+oO6Z7zDqb+uHbtWrvKowDH8Dx7Iw0b7TuWv0a7Tbh712KwmVnbdh9KYs1+c0gCxt6A2XE7PDvSZJpMrhOzBFPUuapEsrvd0+zky5s2bdPYH9fy1uwpQJ4Evbyz3sRPZRUZRJSqdpAAAAAASUVORK5CYII=)
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⇒ y = -2
When x=2, then,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ y = 0
When x=5, then,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ y = 2
Thus we have the following table,
X
-4
-1
2
5
Y
-4
-2
0
2
On plotting these points we have the following graph,
![](data:image/png;base64,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)
Clearly, from the graph (-1, -2) is the solution of the line 2x – 3y = 4
Draw the graph of 2x – 3y = 4. From the graph, find whether x = -1, y = -2 is a solution or not. (Final)
Answer:
Given equation, 2x – 3y = 4
⇒ 3y = 2x-4
When x=-4, then,
⇒ y = -4
When x=-1, then,
⇒ y = -2
When x=2, then,
⇒ y = 0
When x=5, then,
⇒ y = 2
Thus we have the following table,
X | -4 | -1 | 2 | 5 |
Y | -4 | -2 | 0 | 2 |
On plotting these points we have the following graph,
Clearly, from the graph (-1, -2) is the solution of the line 2x – 3y = 4