1. The problem statement, all variables and given/known data Prove that the series: (K from 0 to n) cos(2kx) = [cos(nx)sin((n+1)x)]/sin(x) 3. The attempt at a solution So, on my first attempt I simply wrote out the series as 1+cos2x+cos4x... and looked up the double angle formula's for someinsight on how to simplify the sums into the wanted answer, after not finding any obvious way to continue with this line of thought I stopped. On my second try I tried to convey the series and an exponential expression: (k from 0 to n) e^(2kix), the point being is that I would find the solution to that series and then take the real part of both sides, though again I'm not sure how to find its equivalence. Basically I'm having a hard time showing what the series evaluates to in a closed form with any certain method, any help would be appreciated. Namely what are some good ways of finding closed forms, the exponential series seemed like it would be an easier series to find a closed form for though Its been awhile since complex analysis.