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In this article, we present a geometrical proof of sum of $\cos n\varphi$where $n$ goes from $1$ up to $m$. Although there exist some summation formsand the proofs are simple, they use complex numbers. Our proof comes from ageometrical construction. Moreover, from this geometrical construction weobtain an other summation form.

A geometrical proof of sum of $\cos n\varphi$