My professor said not to bother multiplying out term-by-term but instead use an identity to simplify the $f(x)$
The given is $$f(x)=\sin(x)\cos(x)$$ I'm guessing what my prof. wants us to use is the Pythagorean Identity but that involves $\cos^2(x)+\sin^2(x)=0$ and I can't figure out how that's useful here. Also I don't know what he means by the first four non-zero terms of the series. I am very lost when it comes to power series as the virus has restricted the availability of my professor to answer questions.
HINT
\begin{align*} \begin{cases} \displaystyle\sin(x)\cos(x) = \frac{\sin(2x)}{2}\\\\ \displaystyle\sin(z) = z - \frac{z^{3}}{3!} + \frac{z^{5}}{5!} - \frac{z^{7}}{7!} + \ldots \end{cases} \end{align*}