Prove that $\prod_{k=0}^{n-1}\sin \left( x + k\frac{\pi}{n} \right) = \frac{\sin nx}{2^{n - 1}}$
137844
Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n} \right)$
17241
How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$
138683
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction
104658
proving $\csc^2 \left( \frac{\pi}{7}\right)+\csc^2 \left( \frac{2\pi}{7}\right)+\csc^2 \left( \frac{4\pi}{7}\right)=8$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
65698
Proving $\sum\limits_{k=0}^{n}\cos(kx)=\frac{1}{2}+\frac{\sin(\frac{2n+1}{2}x)}{2\sin(x/2)}$
99314
Closed form of infinite product $ \prod\limits_{k=0}^\infty \left(1+\frac{1}{2^{2^k}}\right)$
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
136652
Closed form expression for the product $\prod\limits_{k=1}^{n}\left(1 - \frac{1}{ak}\right)$
114418
A deduction from $x^n-1=(x^2-1)\prod_{k=1}^{(n-2)/2}[x^2-2x\cos{\frac{2k\pi}{n}}+1]$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
24311
Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$
95673
General formula for $\sin\left(k\arcsin (x)\right)$
79685
For natural $n$, prove $\prod_{k=1}^n \tan\left(\frac{k\pi}{2n+1}\right) = 2^n \prod_{k=1}^n \sin\left(\frac{k\pi}{2n+1}\right)=\sqrt{2n+1}$
85944
Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $
28771
Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
53984
Prove by induction: $\sum\limits_{k=1}^{n}sin(kx)=\frac{sin(\frac{n+1}{2}x)sin\frac{nx}{2}}{sin\frac{x}{2}}$