I proved that all even vectors in a circle than pull outwards have a net force of 0. I'm having trouble with odd vectors.

What I've managed to do so far:

$\displaystyle sin\frac{2k\pi}{n}-sin\frac{2\pi}{n}(n+k)

=sin\frac{2\pi}{n}-sin\frac{2\pi}{n}(k)=0$

I'm having trouble with doing it for cos, plus I don't know if I'm solving it correctly. Thanks