Question

Solve:
sin5x - cos2x + sin x = 0.

Answer 1

x = 10 , 45 degrees.

Explanation:

This seems a tricky one .

I guess we can use sin A + sin B = 2 sin (A+B)/2 cos (A - B) / 2

so sin 5x + sin x = 2 sin 3x cos 2x so our equation becomes

2 sin 3x cos 2x - cos 2x = 0

cos 2x ( 2 sin 3x - 1) = 0

so 2 sin 3x = 1

sin 3x = 1/2

giving 3x = 30 degrees and x = 10 degrees

or cos 2x = 0

so 2x = 90

giving x = 45 degrees.