I have been asked to show that the following is true, and I have been at it now for more time than I care to admit.
Prove that
$\sum_{n = 0}^{N -1} cos(nx) = \frac{sin(Nx/2)}{sin(x/2)} cos(N-1) \frac{x}{2}$
I've done a lot of playing around with identities. I think this one is a little beyond me right this moment. please let's keep this a secret.
I will model the solution of the next one
$\sum_{n = 0}^{N -1} sin(nx) = \frac{sin(Nx/2)}{sin(x/2)} sin(N-1) \frac{x}{2}$
Based on input from the first one.
