Find all solutions of the trigonometric equation Sin2x 2cos

Find all solutions of the trigonometric equation.

Sin(2x) + 2cos(2x) = 2cos^2x

sin2x + 2 cos(2x) = 2 cos^2 x

2 sinx cosx + 2 ( cos^2x - sin^2x) = 2 cos^2x

2 sinx cosx + 2 cos^2x - 2 sin^2x = 2 cos^2 x

2 sinx cosx - 2 sin^2x = 0

2 sinx ( cosx - sinx) = 0

sinx = 0 OR cosx - sinx = 0

x = n pi Or npi + pi/4

x = n pi Or pi (4n + 1)/4

where n = 0,1,2, ....