Trigonometric EquationHard
Question
The general solution of sin x - 3sin 2x + sin3x = cos x - cos2x + cos3x is
Options
A.
B.
C.
D.2nπ + cos-1
Solution
Given, sin3x + sin x - 3sin 2x = cos3x + cos x - 3cos2x
⇒ 2sin 2xcos x - 3sin 2x = cos3x + 2cos2xcos x - 3cos2x
⇒ 2sin 2x(2cos x - 3) = cos 2x(2cos x - 3) (∵ 2cos x - 3 ≠ 0)
⇒ sin 2x = cos 2x
⇒ tan 2x = 1
⇒ 2x = nπ +
⇒
⇒ 2sin 2xcos x - 3sin 2x = cos3x + 2cos2xcos x - 3cos2x
⇒ 2sin 2x(2cos x - 3) = cos 2x(2cos x - 3) (∵ 2cos x - 3 ≠ 0)
⇒ sin 2x = cos 2x
⇒ tan 2x = 1
⇒ 2x = nπ +
⇒
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