Trigonometric EquationHard
Question
The general solution of
sin x -3 sin 2x + sin 3x = cos x - 3 cos 2x + cos 3x is -
sin x -3 sin 2x + sin 3x = cos x - 3 cos 2x + cos 3x is -
Options
A.nπ + π/8
B.
C.(-1)n 
D.2nπ + cos-1 
Solution
(sin x + sin 3x) - 3sin 2x = cos x + cos 3x - 3cos 2x
[2 sin 2x cos x - 3sin 2x] - [2 cos 2x cosx - 3cos 2x] = 0
sin 2x [2 cos x - 3] - cos 2x [2 cos x - 3 ] = 0
cos x =
Not possible
sin 2x = cos 2x
tan 2x = 1 = tan
2x = nπ +
⇒ x =
[2 sin 2x cos x - 3sin 2x] - [2 cos 2x cosx - 3cos 2x] = 0
sin 2x [2 cos x - 3] - cos 2x [2 cos x - 3 ] = 0
cos x =
Not possiblesin 2x = cos 2x
tan 2x = 1 = tan
2x = nπ +
⇒ x =
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