To Find: General solution.

Given: sin x + sin 3x + sin 5x = 0 sin 3x + 2sin 3x cos 2x= 0 sin 3x (1 + 2cos 2x) = 0

[NOTE: sin C + sin D = 2sin (C+D)/2 × cos (C-D)/2]

sin 3x = 0 or cos 2x = = cos()

Formula used: sin= 0 = n , n I, cos = cos = 2k , k I

3x = n or 2x = 2k x = or x = k where n,k I

So general solution is x = or x = k where n, k, I