Question

Find the general solution of the equation

sinx − 3 sin 2x + sin 3x = cos x − 3 cos 2x + cos 3x

(A)  nπ/2 + π/12

(B)  nπ - 5π/12

(C)  nπ/2 + π/8

(D)  nπ ± π/6

Answer 1

Correct option  (C)  nπ/2 + π/8

Given sin x − 3 sin 2x + sin 3x = cos x − 3 cos 2x + cos 3x 

 ⇒ 2 sin 2x cos x − 3 sin 2x = 2 cos x cos 2x − 3 cos 2x

⇒ sin 2x (2 cos x − 3) = cos 2x (2 cos x − 3) 

⇒sin 2x = cos 2x (since cos x ≠ 3/2)