I understand sin(2x)^2 = 1/2 - 1/2cos(2x), due to the double number identity: cos2x = 1 - 2sin(x)^2.

***[My question is how does (cos(2x))^2 = 1/2 + 1/2cos(4x) ???]***

I've tried reworking the identity every which way and can't seem to find out how the two are equivalent. Thanks in advance!