solve :3 sin^2 x-cos^2 x=sin2x

Answer 1

since cos2x = cos^2x - sin^2x, you have

1 - 2cos2x = sin2x
1 - 4cos2x + 4cos^2 2x = sin^2 2x
5cos^2 2x - 4cos2x = 0
cos(2x)(5cos(2x)-4) = 0
cos 2x = 0
cos 2x = 4/5