In my time series homework I had to compute the periodogram of a periodic series and in the solutions we have a step that goes from $\sum_{t=1}^{n-h} \sin(2\pi(\omega(t + h) + \beta))\sin(2\pi(\omega t + \beta))$ to $ \frac{1}{2}\sum_{t=1}^{n-h} \cos(2\pi \omega h)$?
After endless algebra I think I got there via using several identities. Though my prof usually writes them all out, so I am guessing that since he didn't here, I am missing some obvious identity that lets me go there in one step?
Many thanks in advance!