Question

Use a half angle formula to solve for the identity below:
(cos(2x))^2

Answer 1

\[\cos^2\alpha=\frac{1}{2}\left(1+\cos2\alpha\right)\]
which gives you
\[\cos2\alpha=2\cos^2\alpha-1\]
Substitute \(\alpha=2x\).

Answer 2

what if it was (cos(6x))^4

Answer 3

\[\cos^46x=\left(\cos^26x\right)^2\]
You'd apply the half angle formula to rewrite \(\cos^26x=\cdots\), then you'd have \(\left(\cdots\right)^2\). The inside would be a binomial, which could then be expanded.