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Trigonometry, , JEE (Main+Advanced), , Exercise – I, , 8., , Section (A) : Measurement of angle, Fundamental, Identities, sign of trigonometric ratios, allied, angles, graphs of trigonometric ratios, , 9., ,  7 , 0, S1 : ,   410,  3 , c, , 1., , 2., , 1   5 , , S 2 : 112   , , 2  8 , , 0, , Then which statement is correct, (a) only S1, (b) S1 and S2 both, (c) only S2, (d) neither S1 nor S2, , (a), , 5, 4, , (b), , 3., , 4., , 5., , 6., , 7., , , , 11, 4, , 6, ,  cos 2, , , , 4, ,  sec, , 10., , , , 3, , is, , 5, (d) 1, 4, 1, 1, , , sec   tan  sec   tan , (a) 2 tan , (b) 2 sec , (c) 2sin , (d) 2 cos , If a cos   b sin   3 & a sin   b cos   4, then value of a 2  b 2 is, (c) , , (a) 25, (c) 7, , (b) 14, (d) 50, , equal to, , (a), , c, , Value of expression sin 2, , cos(5400   )  sin(6300   ) is equal to, (a) 0, (b) 2 cos , (c) 2sin , (d) sin   cos , 0, 0, sin 420 cos 390  cos(6600 ) sin(3300 ) is, , 11, , then tan A is equal to, 2, 21, 15, (a), (b), 22, 16, 44, 117, (c), (d), 117, 43, If, tan   cot   a then the value of, tan 4   cot 4  is equal to, (a) a 4  4a 2  2 (b) a 4  4a 2  2, (c) a 4  4a 2  2 (d) a 4  4a 2  2, 5, If cos A   and A is not in third quadrant,, 13, then value of sin A  tan A is, 96, 96, (a) , (b), 65, 65, 216, 216, (c) , (d), 65, 65, , 11., , 1, 2, , (c) 1, , (b) 1, (d) 0, , 5, , is not in the second quadrant,, 12, sin(3600   )  tan(900   ), then, ,  sec(2700   )  cos ec(  ), 131, 181, (a), (b), 338, 338, 181, 131, (c) , (d) , 338, 338, , ,  3, ,  7, , tan  x   .cos ,  x   sin 3 ,  x, 2, ,  2, ,  2, , , 3, , , , , , cos  x   . tan ,  x, 2, ,  2, , If tan   , , when simplified reduces to :, (a) sin x cos x, (b)  sin 2 x, 12., , If cos ecA  cot A , , 13., , (c)  sin x cos x, The, , 15., 16., , expression, , , , , ,  3, , , , 3 sin 4 ,     sin 4 (3   )   2 sin 6      sin 6 (5  a ) ,  2, , 2, , , , , , , is equal to, (a) 0, (c) 3, , (b) 1, (d) sin 4  sin 6, , (a) 7, , (b) 8, , sin 2 50  sin 2 100  sin 2 150  .......sin 2 850 sin 2 900 , , (c) 9, 14., , (d) sin 2 x, , 1, 2, , (d) 10, , The value of tan10 tan 20 tan 30...tan 890 is, (a) 1, (b) 0, (c) , , (d), , 1, 2, , Which of the following is correct (a) sin10  sin1 (b) sin10  sin1, , (c) cos10  cos1 (d) sin10  sin1, The sign of the product sin 2 sin 3sin 5 is (a) Negative, (b) Positive, (c) 0, (d) Non negative, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 1

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Trigonometry, , JEE (Main+Advanced), , Section (B) : sin( A  B), cos( A  B), tan( A  B),sin C  sin D,, , cos C  cos D, 2 sin A cos B 2 cos A sin B, 2 cos A cos B, 2sin A sin B, , 17., , Value of, (a) 1, , formulae, , sin130 cos 470  cos130 sin 47 0, is, cos 720 cos120  sin 720 sin120, (b) 0, , 1, (c), 3, 18., , 19., , (d), , The value of, is, (a) -1, (c) 2, If, , sin 240 cos 60  sin 60 sin 660, sin 210 cos 390  cos 510 sin 690, (b) 1, (d) 0, , 2700  A  3600 ,900  B  1800 ,cos A , , 5, 15, , tan B   ,, 13, 8, , 140, 140, (b), 221, 221, 220, 220, (c), (d) , 221, 221, If tan A  tan B  x and cot B  cot A  y, then, cot( A  B ) is equal to, 1 1, 1 1, (a) , (b) , y x, x y, 1 1, (c) , (d) x  y, x y, (a) , , 21., , 22., , 23., , (cos110  sin110 ), The value of, is, (cos110  sin110 ), (a)  tan 3040, (c) cot 214, , 0, , (b) tan 560, , 25., , 26., , 27., , 3, 4, 1, (d), 4, , (a) 1, (c) 3, , (b) 2, (d) 4, , (a) 0, (c) 8, , (b) 2, (d) 1, , tan, tan, ,  , 2, ,  , 2, , is equal to, , (1  tan 80 )(1  tan 37 0 ), The value of, is, (1  tan 220 )(1  tan 230 ), Expression, , (c) cot, 28., , (b), , If 3sin   5sin  , then, , (a) tan, , , , 2, , , , 2, , sin   sin 2, is equal to, cos   cos 2, (b) sec, (d) sin, , , , 2, , , , 2, cos 6 x6 cos 4 x  15cos 2 x  10, The expression, cos 5 x  5cos 3 x  10 cos x, is equal to, (a) cos 2x, , (b) 2 cos x, , (c) cos x, (d) 1  cos x, Section (C) : Multiple and sub-multiple angles, 29., If A lies in the third quadrant and tan A  4  0,, 2, , then 5sin 2 A  3sin A  4 cos A is equal to, , (d) all of these, , 3, and tan A tan B  2, then, 5, 1, (a) cos A cos B  , 5, 2, (b) sin A sin B  , 5, 1, (c) cos( A  B )  , 5, 4, (d) sin A cos B , 5, 0, If A  B  45 , then (1  tan A)(1  tan B ) , If cos( A  B ) , , 3, 2, 3, (c), 4, (a), , 3, , then the value of cos( A  B ) is, , 20., , 24., , (a) 0, (b) 1, (c) 2, (d) 3, 2, 0, Value of sin 45  sin 2 150 is, , 24, 5, 24, 48, (c), (d), 5, 5, tan1550  tan1150, If tan 250  x, then, is, 1  tan1150 tan1150, (a) 0, , 30., , equal to, , 1  x2, 2x, 1  x2, (c), 1  x2, (a), , 31., , (b) , , 1  x2, 2x, 1  x2, (d), 1  x2, (b), , 2 sin 2   4 cos(   ) sin  sin   cos 2(   ) , , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 2

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Trigonometry, , JEE (Main+Advanced), , (a) sin 2, 32., , 33., , (c) cos 2, , 3, the, value, cos A  , then, 4,  A,  A   5A , 16 cos 2    32sin   sin ,  is, 2, 2  2 , , (a) -4, (c) 3, , 1, 2, , If cos    a , ‘a’ is, , 1 3 1 , a  3 , 4, a , , , , (c) 4  a 3 , , 35., , 36., , 1 , , a3 , , 38., of, , (b) -3, (d) 4, , 39., , 1,  , then cos 3 in terms of, a, (b), , 1 3 1 , a  3 , 2, a , , , , , (d)  a 3 , , 1 , , a3 , , 1, t, If sin t  cos t  then tan is equal to :, 5, 2, 1, (a) 1, 2, (b)  , 2, 3, 1, 1, (c) 2,, (d) , 3, 6, If sin   7 cos   5, then tan, , , , 2, , 40., 41., , 42., , is a root of the, , equation, (a) x 2  6 x  1  0 (b) 6 x 2  x  1  0, (c) 6 x 2  x  1  0 (d) x 2  x  6  0, , cos 2 480  sin 2 120 , , (a), (c), 37., , (d) sin 2, , If, , (a), , 34., , (b) cos 2 , , 5 1, 4, 3 1, 4, , (b), , 5 1, 8, , 3 1, (d), 2 2, , The, value, of, the, expression,  , 3  , 7  , 9 , , 1  cos 1  cos  1  cos,  1  cos, , 10, 10, 10, 10 , , , , , is, , 1, (a), 8, 1, (c), 4, , 1, (b), 16, , 43., , conditional identities, , (a) 1, , (b) 2, , 3, 1, (c), (d), 4, 2, 0, 0, If A  tan 6 tan 42 and B  cot 660 cot 780 ,, A, then value of, is, B, 1, (a) 1, (b), 2, 1, 1, (c), (d), 3, 4, tan   2 tan 2  4 tan 4  8 cot 8 , (a) tan , (b) cot , (c) cot16, (d) 16 cot , , In any triangle ABC, which is not right angled, ,  cos A.cos ecB.cos ecC is equal to, , (a) 1, (c) 3, , (b) 2, (d) 0, , If, , A B C , , 3, , then, 2, , cos 2 A  cos 2 B  cos 2C is equal to, (a) 1  4cos A cos B cos C, (b) 4 sin A sin B sin C, (c) 1  2 cos A cos B cos C, (d) 1  4sin A sin B sin C, If       0, then sin 2  sin 2   sin 2, is equal to, (a) 4 cos  cos  cos , , (b) 1  4 cos  cos  cos , (c) 4sin  sin  sin , , (d) 4 sin  sin  sin , Section (E) : Sum of sine and cosine series, product of, cosine series, range of trigonometric functions, 44., The, value, of, cos 0  cos, , is, , (d) 0, , Section (D) : sin  sin(600   )sin(60   ),, , cos 200  8sin 700 sin 500 sin100, is equal to :, sin 2 800, , 45., , , , 9, , (a), , 1, 2, , n, , sides, ,  cos, , 2, 3, 5, 6, 7, 8,  cos,  cos,  cos,  cos,  cos, 9, 9, 9, 9, 9, 9, , (b) , , 1, 2, ,  is, , any, , (c) 0, (d) 1, If  is the exterior angle of a regular polygon of, and, , constant,, , then, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 3

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Trigonometry, , JEE (Main+Advanced), , sin   sin(   )  sin(  2 )  ..... up to n, , terms =, (a) sin n, 46., , 47., , 48., , (c) 2n, , The, , 51., , 52., , value, , 2, 4, 8, 16, is :, cos cos, cos, cos, cos, 10, 10, 10, 10, 10, , , , 10  2 5, 64, , cos( / 10), 16, , (b) , , (a) n , , 54., , (a) 3, (c) 5, The, , (d) , , values, ,  2, ,  2, , cos x cos ,  x  cos ,  x  are  3, ,  3, , 1 1, 1, (a)  ,, (b) 0,, 4 4, 4, (c) 0,1, (d) 1,1, , The, , greatest, , and, , teast, , value, , y  10 cos x  6sin x cos x  2sin x are, 2, , 2, , of, , 55., , 56., of, , y  1  2sin x  3cos x is, 16, 13, (a), (b), 3, 3, , 4, , , , 8, , , n  I (b) n , , general, , cot 3  cot   0 is, n, ,n I, 2, , of, , (d) (2n  1), , , , 2, , general, , , , 2, , solution, , ,n I, , solution, 2, , general, , , , 2, , ,n I, of, , equation, , the, , equation, , ,n I, , 2 cos 2 x  3.2 cos x  4 is, (a) x  2n , n  I, (b) x  n , n  I, n, (c) x , ,nI, 4, n, (d) x , ,nI, 2, The, , ,n I, , 4, , , n  I (d) 2n , , (a) n , n  I, , The, , , , of, , solution, , of, sin x  sin 5 x  sin 2 x  sin 4 x is :, , equation, , n, n, (b), ;n I, ;n I, 2, 5, n, 2n, (c), (d), ;n I, ;n I, 3, 3, cos 4 x cos8 x  cos 5 x cos 9 x  0 if, (a) cos12 x  cos14 x, (b) sin13 x  0, (c) sin x  0, (d) all of these,  , If x  0,  , the number of solutions of the,  2, equation sin 7 x  sin 4 x  sin x  0 is :, (a), , 57., , respectively, (a) 11,1, (b) 10,2, (c) 12,-4, (d) 11,-1, The difference between maximum and minimum, value, of, the, expression, 2, , The, , , , (c) n  ( 1) n, , cos( /10), 16, , (b) 4, (d) 8, extreme, , (c) n , , (b), , 10  2 5, 16, The maximum value of 12 sin   9 sin 2 , (c), , 50., , (d) 0, , 2, 4, 6, cos, cos, cos, , 7, 7, 7, 1, 1, (a), (b), 4, 8, 1, 1, (c), (d), 16, 32, , 2, 3, 4, 5, cos cos, cos, cos, cos, , 11, 11, 11, 11, 11, 1, 1, (a), (b), 4, 8, 1, 1, (c), (d), 16, 32, , (a), , 49., , (b) sin n, , Section (F) : Solution of standard trigonometric, equations, Solution of trigonometric, equations of type-I, II, III, 53., General solution of equation sin 2 x  1 is, , 58., , 59., , (a) 3, (c) 6, General, , (b) 5, (d) 2, solution, , tan 3x  tan 2 x,  1 is, 1  tan 3 x tan 2 x, , of, , equation, , (c) 7, (d) 8, ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 4

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Trigonometry, , JEE (Main+Advanced), , (a) n , 60., , 61., , , , , n  I (b) n , , 4, (c) n , n  I, , 4, , (a) 2n , , ,nI, ,  n , , n  N , then greatest value of n is,  2 , , in 0,, , (a) 8, (c) 13, , cos 3, 1,  if, 2 cos 2  1 2, , , , 3, , (c)   2n , , (b) 10, (d) 15, , , , (c) 2n , , 67., , , n  I (b)   2n , , n  I (d)   n , , , , 3, , , , (b) 4 real solutions, (d) 8 real solutions, of, solution, of, , 63., , 64., , (a) 4, (b) 8, (c) 12, (d) 16, If tan   tan 4  tan 7  tan  tan 4 tan 7 ,, , 68., , 16cos x  16sin x  10 in x  [0, 3 ] is equal to 2, , 2, , 69., , 66., , General, , solution, 5sin   2 cos   5 is, , ,n I, , 2, ,n I, 7, sin 2 x  2sin x cos x  3cos 2 x  0 if, (a) tan x  3, , (d) x  n , , , , 4, , , , 4, , , , , , 2, , ,n I, , 2, ,n I, 3, , The most general solution of, , 1, is :, 2, 7, n , ,n I, 4, 7, n  ( 1) n, ,n I, 4, 7, 2n , ,n I, 4, , n  ( 1) n , n  I, 4, , cos  , , (d), , tan   1 and, , The most general value of  which satisfies both, the equations tan   3 and cos ec  , is -, , equation, , ,n I, , (d) x  n  ( 1)n sin 1, , (b), , 70., , ,n I, , ,n I, 3, sin 2 x  cos 2 x  2  sin 2 x if, n, (a) x , ,nI, 2, 1, (b) tan x , 2, , (c), , of, , 2, , 2, ,n I, 7, , (d) 2n  2 where   tan 1, , (a), , Section (G) : Solution of trigonometric equation of, type IV, V, simultaneous equations, use of boundness, 65., General, solution, of, equation, , 3 sin   cos   3 is, , , (a) n   (1) n , n  I, 6, 4, , , (b) 2n   (1) n , n  I, 6, 4, (c) 2n , n  I, , , (d) n   (1) n , n  I, 6, 4, , ,n I, , (c) x  (2n  1), , then  , , n, n, (a), (b), ,n I, ,n I, 4, 7, n, (c), ; n  6(2k  1),(n, k  I ), 12, (d) n , n  I, , , , (c) x  n , , ,n I, , (a) 2 real solutions, (c) 6 real solutions, Total, number, , 2, , (b) x  n , , ,n I, , 6, 6, The equation sin 3  4sin  ,sin 2 ,sin 4 in, 0     has :, , , , (b) 2n  2 where   tan 1, , If 2 tan 2 x  5sec x  1  0 has 7 different roots, , (a)   n , , 62., , (d) , , , , (a) n , , 4, 2, ; n  I (b) n , ;n I, 3, 3, , 2, 3, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 5

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Trigonometry, , JEE (Main+Advanced), , 71., , 4, 2, ; n  I (d) 2n , ;n I, 3, 3, If 0  x  2 , 0  y  2 and sin x  sin y  2, then the value of x  y is (a) , , 72., , (b), , (c) 3, , 74., , 5, , The, , set, , of, , 77., , values, , 3, , of, , x, , 78., , 79., , for, , which, , sin x.cos x  cos x.sin x, 0  x  2 , is 3, , (c), , n, ,n I, 2, , 2sin x  3  0 is, 2, 4 , , (a)  2n , , 2n , ,n I, 3, 3 , , , 2 , , (b)  2n  , 2n , ,n I, 3, 3 , , , , , (c)  2n  , 2n   , n  I, 3, 3, , , , (d)  2n , 2n   , n  I, 3, ,  , ,  4,  3 , (d)   ,, , 2 , , , 80., , (b)  0,, , (a) ( ,    ), ,   5 , , , 3 6 , , (c) , , , , 2, , (d) 20 m, , If the angles of elevation of the top of a tower, from two points distant a and b from the base, and in the same straight line with it are, complementary, then the height of the tower is, (a) ab, , (b), , (c), , (d), , a, b, , ab, a, b, , From the top of a cliff 25 m high the angle of, elevation of a top of tower is found to be equal, to the angle of depression of the foot of the, tower. The height of the tower is (a) 25 m, (b) 50 m, (c) 75 m, (d) 100 m, A tree 12 m high, is broken by the wind in such, a way that its top touches the ground and makes, an angle 600 with the ground. The height from, the bottom of the tree from where it is broken by, the wind is appoximately, (a) 5.57 m, (b) 5.21, (c) 5.36, (d) 5.9, AB is a vertical pole and C is the middle point., The end A is on the level ground and P is any, point on the level ground other than A. The, portion CB subtends an angle  at P. If, , 1, 9, 5, (c) tan 1  , 9, (a) tan 1  , , inequality log sin  (2  cos 2 x)  log sin  (1  sin x),, where x  (0, 2 ) and x , , 15, m, 3, , (b) 15m, , AP : AB  2 :1, then  is equal to -, ,  , , , 4 , , Let   , then the solution set of the, 3, (c) , , 76., , 4, , Section (H) : Trigonometric Inequalities, Set of values of x satisfying inequality, , (a) (0,  ), , 75., , 2, , The solution set of equation cos x  1  sin x, is (a) n , n  I, (b) 2n , n  I, (d), , (a) 15 3m, , , , (d) 0, , (c) 4n , n  I, , 73., , the roadway between the pillars, the angle of, elevation of the top of pillars are 600 and 300 ., The height of the pillars is -, , (c) 2n , , , is, , 4, 9, 2, (d) tan 1  , 9, (b) tan 1  , ,    , ,    ,  ,  2 2, ,     , (d)  0,    ,  ,  2 2 , , (b)   ,, , Section (I) : Height and Distance, Two pillars of equal height stand on either side, of a roadway which is 60 m wide. At a point in, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 6

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Trigonometry, , JEE (Main+Advanced), , Answer Key, 1, c, 11, d, 21, d, 31, c, 41, b, 51, a, 61, b, 71, a, , 2, c, 12, b, 22, c, 32, c, 42, d, 52, a, 62, d, 72, b, , 3, b, 13, c, 23, c, 33, b, 43, c, 53, b, 63, c, 73, b, , 4, a, 14, a, 24, b, 34, b, 44, d, 54, d, 64, c, 74, b, , 5, c, 15, b, 25, d, 35, b, 45, d, 55, b, 65, a, 75, d, , 6, b, 16, a, 26, d, 36, b, 46, b, 56, c, 66, c, 76, a, , 7, d, 17, d, 27, c, 37, b, 47, d, 57, d, 67, c, 77, b, , 8, a, 18, a, 28, b, 38, b, 48, b, 58, b, 68, c, 78, b, , 9, c, 19, b, 29, a, 39, a, 49, b, 59, d, 69, c, 79, a, , 10, b, 20, c, 30, a, 40, b, 50, a, 60, d, 70, c, 80, d, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 7