<s>[INST] Express $f(x) = x^2 \cos(2x) + \sin^2(x)$ as a power series 
Express $f(x) = x^2 \cos(2x) + \sin^2(x)$ as a power series

What I know:

I know that $$x^2\cos(2x) = x^2 \cdot \sum_{n=0}^{\infty} {(-1)^n \cdot \frac{(2x)^{2n}}{(2n)!}} = \sum_{n=0}^{\infty} {(-1)^n \cdot \frac{2^{2n} \cdot x^{2n+2}}{(2n)!}}$$

But how do we find what $\sin^2(x)$ is in terms of a power series?
 [/INST] HINT
$$ \sin^2 {x} = 1 - \cos^2 {x} = \dfrac{1 - \cos(2x)}{2}$$
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