Hello,

I'm trying to show that $\displaystyle \sum _{j=1}^{N-1} \sin \left(\frac{j \pi y}{N}\right)\sin\left(\frac{j \pi k}{N}\right)=0$, if y does not equal k (with y and k both being integers). I've tried using the trig identity for the product of sines. That gives $\displaystyle \sum _{j=1}^{N-1} \left [\cos\left (\frac{j \pi (y-k)}{N}\right ) - \cos\left (\frac{j \pi (y+k)}{N}\right )\right ]$, but I'm still stuck there.

Any ideas?