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M.K. MATHEMATICS (M.:8826181724), , CLASS:-XI, , TRIGONOMETRY, , PRACTICE EXERCISE 3.1, Q 1.If sin A , , 3, 9, , , and cos B , , 0 < A < , 0 < B < , find the values of the following :, 5, 41, 2, 2, , (i) sin (A – B), , (ii) sin (A + B), , 133, 187, (ii), (iii), 205, 205, 3, Q 2.If sin A  , 0 < A <, 5, 1. (i), , (i) sin (A – B), 2. (i), , (iv) cos (A + B), , 156, 84, (iv), 205, 205, , 12, 3, and cos B =, ,<B<, , find the following :, 2, 13, 2, , (ii) cos (A + B), , (iii) tan (A – B), , 16, 33, 16, (ii), (iii), 65, 65, 63, , Q 3.If cos A , , 4, 12 3, , cos B , ,, < A, B < 2, find the values of the following :, 5, 13 2, , (i) cos (A + B), 3. (i), , (iii) cos (A – B), , 33, 65, , (ii), , (ii) sin (A – B), , 16, 65, , Q 4.Find the values of the following :, (i) sin 75, 4. (i), , (ii) cos 75, , (iii) sin 15, , (iv) cos 15, , (iii) tan 105, , (iv) tan, , 3 1, 3 1, 3 1, 3 1, (ii), (iii), (iv), 2 2, 2 2, 2 2, 2 2, , Q 5.Find the values of the following :, (i) tan 15, 5. (i), , 3 1, (ii), 3 1, , (ii) tan 75, , 3 1, 3 1, (iii) , (iv), 3 1, 3 1, , 13, 12, , 3 1, 3 1, , Q 6.Prove that tan 75 + cot 75 = 4, Q 7.Evaluate the following :, , 7, , 7, , cos  cos sin, 12, 4, 12, 4, 2, , 2, , cos  sin sin, (iii) cos, 3, 4, 3, 4, (i) sin, , 7. (i), , (ii) sin, , , , , , cos  cos sin, 4, 12, 4 12, , 3 1, 3, 3, (ii), (iii) , 2, 2, 2 2, , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 2

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M.K. MATHEMATICS (M.:8826181724), , CLASS:-XI, , TRIGONOMETRY, , , , , , ,  , ,  A  cos   B   sin   A  sin   B   sin(A  B), 4, , 4, , 4,  4, , , Q 8.Prove that : cos , Q 9.Prove that :, , , , , ,  x   cos   x   2 cos x, 4, , 4, , , (i) cos , , Q 10.Prove that :, ,  3, ,  3, ,  x   cos   x    2 sin x,  4, ,  4, , , (ii) cos , , sin(x  y) tan x  tan y, , sin(x  y) tan x  tan y, , , , tan   x , 2, 4,  1  tan x , , , Q 11.Prove that :, , , ,   1  tan x , tan   x , 4, , Q 12.Prove that :, (i) tan 3A tan 2A tan A = tan 3A – tan 2A – tan A, Q 13.If A  B , , (ii) cot A cot 2A – cot 2A cot 3A – cot 3A cot A = 1, , , ¸prove that :, 4, , (i) (1 + tan A)(1 + tan B) = 2, Q 14.Prove that :, , (ii) (cot A – 1)(cot B – 1) = 2, , tan(A  B) sin 2 A  sin 2 B, , cot(A  B) cos 2 A  sin 2 B, , Q 15.Prove that : sin2 6x – sin2 4x = sin 2x sin 10x, Q 16.Prove that : cos2 2x – cos2 6x = sin 4x sin 8x, Q 17.Prove that : tan 70 = tan 20 + 2 tan 50, , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 3

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M.K. MATHEMATICS (M.:8826181724), , CLASS:-XI, , TRIGONOMETRY, , PRACTICE EXERCISE 3.2, Q 1.Prove the following identities, (i) sin8   cos 8   (sin2   cos 2 )(1  2 sin2  cos 2 ), (ii) cot 4   cot 2   cos ec 4   cos ec 2, (iii) 2 sec 2   sec 4   2 cos ec 2  cos ec 4   cot 4   tan4 , (iv) (sin   cos ec)2  (cos   sec )2  tan 2   cot 2   7, Q 2.Prove the following identities :, (i) (1 + cot  - cosec )(1 + tan  + sec ) = 2, (ii), , tan   sec   1 1  sin , , tan   sec   1, cos , , Q 3.If a cos  + b sin  = x and a sin  - b cos  = y, prove that a2 + b2 = x2 + y2., Q 4.If, , sin A, cos A,  p and,  q , find tan A and tan B., sin B, cos B, , p q2 1, q2 1, 4. tan A  , and tan B  , q 1  p2, 1  p2, Q 5.If sec  + tan  = p, obtain the value of sec , tan  and sin  in terms of p., 5. sin  , , p2 1, p2  1, , Q 6.Prove that :, 3(sin  - cos )4 + 6(sin  + cos )2 + 4(sin6  + cos6 ) – 13 = 0, Q 7.Prove that sec2  + cosec2   4., , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 4