Cotes Circle Property

$x^{2n}+1=\left[{x^2-2x\cos\left({\pi\over 2n}\right)+1}\right]$

$\times \left[{x^2-2x\cos\left({3\pi\over 2n}\right)+1}\right]\times\cdots\times$

$\times \left[{x^2-2x\cos\left({(2n-1)\pi\over 2n}\right)+1}\right].$

$x^{2n}+1=\left[{x^2-2x\cos\left({\pi\over 2n}\right)+1}\right]$
$\times \left[{x^2-2x\cos\left({3\pi\over 2n}\right)+1}\right]\times\cdots\times$
$\times \left[{x^2-2x\cos\left({(2n-1)\pi\over 2n}\right)+1}\right].$