I keep trying to find the power reducing formula for sin^4(x), but I can't seem to get all the fractional parts correct.

Question

The answer I should be getting is:

sin^4(x)=(1/8)cos4x-(1/2)cos2x+(3/8)

I can only get this far knowing feeling confident. When I go further I start making mathematical errors.

((1-cos2x)/2)*((1-cos2x)/2)