Hi, just a quick question.

Doing a bit of Fourier Series and I've come across this integral, is there a best way to go about doing this?

$\displaystyle \frac{2}{\pi} \int_0^{\pi} \cos{(x)} \sin{(nx)} dx$, where $\displaystyle n$ is an integer $\displaystyle 0 \leq n \leq \infty$.

I've attempted by using the product to sum formulas, but this just ends up with at least two sides of tricky algebra.

Has anyone come across this before, or have any helpful 'shortcuts'?

Thanks in advance for your help