Prove $\prod_{i=1}^{n-1} \sin(i\pi/n) = 2^{1-n} n$ without complex functions.
18285
Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
12653
Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$
111976
Prove that a product of two complex numbers has zero imaginary part
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
30480
Continued product in $\sin$ series
146047
Proving that $\cos(2\pi/n)$ is algebraic
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
11335
Proving Binomial Identity without calculus
126701
How to prove that $d \sin(x)/dx = \cos(x)$ without circular logic such as L'Hôpital's rule?
32823
Prove $\forall n \in \mathbb{N}: \int_{0}^{\frac{\pi}{2}} |\frac{\sin(nx)}{x}|dx \geq \frac{2}{\pi}\sum_{k=1}^{n}\frac{1}{k}$
24391
$\arcsin$ written as $\sin^{-1}(x)$
87242
Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
44614
How to prove the closed form of the integral $\int \frac {dx}{\prod_{r=0}^n (x+r)}$
37040
Prove reduction formula for $\int \cos^n (x)\sin^m (x) \, dx$
35529
Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$
110826
prove that : $ i = \sqrt {-1}\ $
79685
For natural $n$, prove $\prod_{k=1}^n \tan\left(\frac{k\pi}{2n+1}\right) = 2^n \prod_{k=1}^n \sin\left(\frac{k\pi}{2n+1}\right)=\sqrt{2n+1}$