Trigonometric problem from physics – math.stackexchange.com

I am trying to prove that: $1+\cos a+\cos 2a+\cos3a+\cos4a=0$ where $a=\frac{2\pi}5$ (pentagon arrangement). Actually this is true for any $n>1$: $1+\cos a+\cos2a+\dots+\cos(n-1)a=0$ (polygon) ...

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