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Maths IIT-JEE ‘Best Approach’, TRIGONOMETRIC EQUATION, Two types of solution, , Principal solution, 0  2  , , General solution, (6 forms), , GENERAL SOLUTION OF, TRIGONOMETRIC EQUATION:, (i), , , If sin  = sin , = n + (–1) n , , MCSIR, , Trigonometric Eq. (Ph-2), Note (1) First check for real solution, (2) Avoid squaring, Ex., , If cos cos , = 2n where [0,], n I., , (iii), , If tan = tan , , , ,   , = n + where   ,  n I.,  2 2, , (iv), , If sin2 = sin2  = n, , (v), , cos 2 = cos 2  = n , , (vi), , tan2 =, , tan2, , 3 cos x + sin = 2, , Ex., , sin x + cos x = 1.5, , Ex., , (sec x –1) =, , Ex., , 4 cos x + 3 sin x = 5., , Ex., , 1+ sin3 x + cos3 x =, , Ex., , Solve : 3 3 sin3 x + cos 3 x + 3 3 sin x, cos x = 1., , 2 cos x . cos 2x = cos x, , Ex., , cot x – cos x = 1 – cot x. cos x, , Ex., , (1 –tan) (1 + sin2) = 1 + tan., , Ex., , Find t he ge ner al s o lu t io n o f t he, trigonometric equation, cos4x + 6 = 7 cos 2x and also find the, sum of all the solution in [0,100], Type -2, Solving trigonometric equations by, introducting an Auxilliary argument, Equation of the form of, a cos + b sin= c., , , , 2  1 tan x., 3, sin 2x., 2, , Type-4, Solving equations by transforming a, product of trigonometric functions into, a sum., Ex., , Note :  is called the principal angle, , Ex., , , , Type-3, Solving equations by Transforming a sum, of Trigonometric fum of Trigonometric, functions into a product., ,  = n , , TYPES OF TRIGONOMETRIC, EQUATIONS, Type -1, Solution of trigonometric equation by, factorisation or equation which are, expressed in quadratic form or which, can be expressed in quadratic form., , 2, , Ex., ,   , where    ,  ,n I.,  2 2, , (ii), , , sin x + cos x =, , General solution of the trigonometric, equation, sin x + sin 5x = sin 2x + sin 4x, is, (A), , n, 3, , (B), , 2n, 3, , (C) 2n, , (D) n, , Ex., , Find all value of , between 0 & ,, which satisfy the equation; cos . cos 2, . cos 3  = 1/4., , Ex., , Number of solutions of the equation, sin, x + 2 sin 2x = 3 + sin 3x in [0,], (A) no solution (B) infinite solution, (C) exactly one solution, (D) two solutions, , Ex., , Find the number of solution of the, equation in [0,2], tan(5cos ) = cot (5sin ), , Ex., , cos 2x + cos2 2x + cos2 3x + cos2 4x = 2., , Ex., , sin 6x, = 8 cos x. cos 2x. cos 4x, sin x, Type -5, Solving equations by change of variable, or by substitution method, , Get 10% Instant Discount On Unacademy Plus [Use Referral Code: MCSIR], , 2

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Maths IIT-JEE ‘Best Approach’, , MCSIR, , Ex., , sin4 2x + cos4 2x = sin2x . cos2x., , Ex., , cosx + cos 2x + cos 3x = 3, , Ex., , Solve for x and y,, 1 – 2x –x2 = tan2 (x + y) + cot 2 (x +y)., , Ex., , Number of ordered pair satisfying the, inequality, 2cos ec, , 2, , z, , Trigonometric Eq. (Ph-2), Q., , Q., , y 2  2y  2 2., , Type-6, Solution of trigonometric equation of the, , Q., , cos( – ) = 1 and cos( + ) = 1/e,, where ,   [–, ], numbers of pairs, of ,  which satisfy both the equations, is, [JEE 2005 (Screening)], (A) 0, (B) 1, (C) 2, (D) 4, , Q., , If 0 <  < 2, then the intervals of values, of  for which 2sin2  – 5sin + 2 > 0, is, , form of f(x) =   x , Ex., Ex., , 1  cos x  sin x ., , , , 2sin  3x    1  8 sin 2x cos 2 2x, 4, , , TRIGONOMETRIC INEQUALITIES, AND SYSTEM OF INEQUALITY, 1., , , , sinx > 0, , 2., , sin x >, , 1, 2, , , , 0<x<, , , 5, x, 6, 6, ,     5, , (A)  0,    , 2 ,  6  6, , , ;, ,   5 , (B)  , , 8 6 , , 7, , , x, 6, 6, 3., , x, , x 1, log 2  sin   1  0 < sin , 2, 2 2, , , 4., , 1, cos x <  ;, 2, , 5., , tanx > 0, , Q., , tan2 x –, , Q., , , , ;, , , , 3  1 tan x +, , Q., , 5  2sin x 6 sin x –1., , cos x. cos y =, , 3, 4, , 1, 4, cos (x + y) = 1, , and, , sin x . sin y =, (2), ,  41 , , , (D) ,  48 , , 3 <0, , SOLVING SYSTEM OF, TRIGONOMETRIC EQUATIONS, (1), ,      5 , (C)  0,    , ,  8 6 6 , , 3, 5, x, 4, 4, , 0<x<, 2, , cos (x + y) =, , Find real values of x for which,, 27 cos 2x . 81 sin 2x is minimum ., Also find this minimum value., [REE 2000, 3], The number of integral values of k for, which the equation 7cosx + 5sinx =, 2k + 1 has a solution is, (A) 4, (B) 8, (C) 10, (D) 12, [JEE 2002 (Screening), 3], , Q., , [JEE 2006, 3], For x (0, ), the equation sin x + 2, sin 2x – sin 3x = 3 has :, [JEE Adv. 2014], (A) infinitely many solutions, (B) three solutions, (C) one solution, (D) no solution, If 0  x  2, then the number of real, values of x, which satisfy the equation, cosx + cos2x + cos3x + cos4x = 0, is, [JEE Main 2016], (A) 3, (B) 5, (C) 7, (D) 9, , and, , 1, 2, , Get 10% Instant Discount On Unacademy Plus [Use Referral Code: MCSIR], , 3