How to prove that $ \arctan x + 2 \arctan(\sqrt{1 + x^2} - x) = \frac{\pi}{2} $
1859
Proving $\arctan(\sqrt{x^2+1}-x)=\frac{\pi}{4}-\frac{1}{2}\arctan(x)$
103757
how can I prove that $\frac{\arctan x}{x }< 1$?
145521
Why does $\arctan(x)= \frac{1}{2i}\log \left( \frac{x-i}{x+i}\right)+k$?
5747
$\cos(\arcsin(x)) = \sqrt{1 - x^2}$. How?
12158
Show that $\arctan\frac{1}{2}+\arctan\frac{1}{3}=\frac{\pi}{4}$
71796
Proving $\rm \frac i 2 \ln\frac {x+i}{x-i}=\arctan x$ .
46948
Definite integral $\int_{\frac{1}{a}}^a \frac{\arctan(x)}{x}$
35529
Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$
7296
Prove $(1-\cos x)/\sin x = \tan x/2$
103144
Is there a way to write this expression differently: $\arctan 1/(1+n+n^2)$?
2491
For $0 < x < \pi/2 $, prove that $x + \frac{x^{3}}{3} <\tan x $
60230
Prove that $\frac{1+\sin\theta+i\cos\theta}{1+\sin\theta-i\cos\theta}=\sin\theta+i\cos\theta$
23397
Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$
97011
Proving that $\prod_{k=1}^{n}\tan\left(\frac{\pi k}{2n+1}\right)=\sqrt{2n+1}$ using geometry
102932
Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$?
48586
Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
100817
Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$