A Very Cool Trigonometric Identity

We prove a surprising trigonometric identity using the sum-to-product identities for sin and cos. Sum-to-product identities: https://en.wikipedia.org/wiki/List_of... Half-angle formulae: https://en.wikipedia.org/wiki/List_of... 00:00 Intro 00:25 Idea of the proof (n=5) 05:45 Proof for odd n 08:49 Proof for even n 11:52 Another method: complex numbers