BITSAT2017MathematicsTrigonometric EquationsActual
The general solution of sin x - 3 sin 2 x + sin 3 x = cos x - 3 cos 2 x + cos 3 x is
Options
- An π + π 8
- Bn π 2 + π 8
- C- 1 n n π 2 + π 8
- D2 h π + cos - 1 3 2
Correct answer
B. n π 2 + π 8
Step-by-step solution
We have, sin x - 3 sin 2 x + sin 3 x = cos x - 3 cos 2 x + cos 3 x ⇒ sin x + sin 3 x - 3 sin 2 x = cos x + cos 3 x - 3 cos 2 x ⇒ 2 sin 2 x cos x - 3 sin 2 x - 2 cos 2 x cos x + 3 cos 2 x = 0 ⇒ sin 2 x ( 2 cos x - 3 ) - cos 2 x ( 2 cos x - 3 ) = 0 ⇒ ( sin 2 x - cos 2 x ) ( 2 cos x - 3 ) = 0 ⇒   sin 2 x = cos 2 x    [ ∵ cos x ≠ 3 / 2 ] ⇒   2 x = 2 n π ± π 2 - 2 x ⇒   x = n π 2 + π 8 [ ∵ neglect - ve sign]