Question

Write sin^2(x)*cos^2(x) as a single power of cosine, show work

Answer 1

This is what you're looking for if I'm not mistaken
sin²x + cos²x = 1
So:
sin²x = 1 - cos²x

∴ sin²x * cos²x = (1 - cos²x) * cos²x
= cos²x.(1 - cos²x)
(= cos²x - cos⁴x)