How to algebraically solve 2cos² x = sin 2x

How would I solve 2cos² x = sin 2x for for 0 ≤ x ≤ π in terms of π.

Thanks!

First, you need to simplify this equation to have a trigonometric function of the same expression:

2cos² x = sin 2x
2cos² x = 2 sin x cos x
2cos² x - 2 sin x cos x = 0
2cos x (cos x - sin x) = 0

And the solutions are cos x = 0 or cos x = sin x

x = π/2 or x = π/4

These are the two solutions.

2cos^2 x=2sinx.cosx , cosx(cosx-sinx)=0 , cosx=0 or tanx=1 , x=pi/2 or pi/4