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Prove the identity on sines

Source:

September 22, 2010

trigonometryalgebrapolynomialTrigonometric IdentitiesIMO Shortlist

Problem Statement

Prove that for all

n \in \mathbb N

the following is true:

2^n \prod_{k=1}^n \sin \frac{k \pi}{2n+1} = \sqrt{2n+1}