x^{2n+2}-1=(x^2-1)\prod_{k=1}^{n-1+1} \Bigg(x^2-2x \cos \Bigg(\frac{k \pi}{n+1}\Bigg)+1\Bigg) \Rightarrow x^{2n}-1+(x^2-1)=(x^2-1)\Bigg(\prod_{k=1}^{n-1} x^2-2x\cos\frac{k\pi}{n}\Bigg)+x^2-2x\cos\frac{k\pi}{n+1}