Trigonometric double angle formulas problem I want to simplify the answer to an equation I had to compute, namely, simplifying $\sin^2 (2y) + \cos^2 (2y)$. I know that $\sin^2 (y) + \cos^2 (y) = 1$ but is there anything like that I can use at all?

In general $$\sin^2(\color{red}{\rm something}) + \cos^2(\color{red}{\text{the same thing}})=1.$$So your expression is just $1$.
