Express cos^2xsin^2xin terms of cosxraised to the first power.

Here is my first attempt at this. I'd like for someone to look over my steps and help me make sure I did this right.

Using double angle formulas for lowering powers:

(cos^2x)(sin^2x) = ((1+cos2x)/2) ((1-cos2x)/2)

= (1 - cos2x + cos2x - cos^2(2x))/4

= (1 - cos^2(2x))/4

= (1/4) (1 - cos^2(2x))

= (1/4) - (1/4) ((1+cos4x)/2)

= (1/4) - (1/8) + (1/8) cos4x

= (1/8) + (1/8) cos4x as final answer.