How to prove $a\cos\left(\frac{2n\pi}{N}\right) \neq \cos\left(\frac{(n-1)\pi}{N}\right)$ for $n = \{0,1,...,N-1\}$ where $a$ is a scalar and $N \geq 3$.
I proceeded like this
$a\cos\left(\frac{2n\pi}{N}\right) = \cos\left(\frac{(n-1)\pi}{N}\right)$
if $\cos\left(\frac{2n\pi}{N}\right) \neq 0$ then $a = \sin\left(\frac{2\pi}{N}\right) + \tan\left(\frac{2n\pi}{N}\right)\cos\left(\frac{2\pi}{N}\right)$
How to proceed further?