Showing that $1-\cos(x) <\frac{x^2}{2}$ holds
107601
Use of inequality $1 - \cos (x) \leq x^2 /2$
138575
Proof that $\cos^2(x)\cosh^2(y) + \sin^2(x)\sinh^2(y) = -1 + \sin^2(x) - \sinh^2(y)$
142114
Limit as $x\to 2$ of $\frac{\cos(\frac \pi x)}{x-2} $
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
105622
How to show $ \sin x \geq \frac{2x}{\pi}, x \in [0, \frac{\pi}{2}]$?
97553
Continuity of $\frac{2xy}{x^2+y^2}$ at $(0,0)$
44119
Prove that $\cos (A + B)\cos (A - B) = {\cos ^2}A - {\sin ^2}B$
129847
Show that $\forall (x,y)$ in the first quadrant: $\frac {x^2+y^2}{4}\leq e^{x+y-2}$
7296
Prove $(1-\cos x)/\sin x = \tan x/2$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
87055
How to prove $\frac{x}{1+x^2}0$?
90556
Proof of the unbounded-ness of $\sum_{n\geq 1}\frac{1}{n}\sin\frac{x}{n}$
24656
Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
2491
For $0 < x < \pi/2 $, prove that $x + \frac{x^{3}}{3} <\tan x $
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
69803
An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$