Question

rewrite sin^4 (x) so it only involves the first power of cosine. start with the left hand side

Answer 1

\[\sin^4x=(\sin^2x)^2=(1-\cos^2x)^2\]
and expand

Answer 2

Alternatively, you can use the half-angle identity:
\[\sin^4x=(\sin^2x)^2=\left(\frac{1}{2}-\frac{1}{2}\cos2x\right)^2\]

Answer 3

The question also asks to rewrite the equation as a product of two squared terms in the second step. How do i do this?

Answer 4

You can expand on what @SithsAndGiggles in the first comment, and use the difference of squares identity, i.e. \((x^2 - a^2) = (x-a)(x+a)\)