Let $l\in\mathbb{Z}$ and $N\in\mathbb{N}$. I need to prove the following: \begin{equation} \sum_{j=0}^{N-1}\cos\left(l\frac{\left(2j+1\right)\pi}{2N} \right)=0 \end{equation} I tried to use Euler formula and then sum the first $N$ terms of the geometric serie I get, but it didn't work. Any ideas?
Proving $\sum_{j=0}^{N-1}\cos\frac{\left(2j+1\right)\pi}{2N}=0$
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trigonometry
summation