Prove $\cos(x)<\frac{\sin^2(x)}{x^2}$
96388
Prove $\sin(x)\tan(x) > x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$
31792
show that $\int_{0}^{\infty}\frac{x\cos ax}{\sinh x}dx=\frac{\pi^2}{4} \operatorname{sech}^2 \left(\frac{a\pi}{2}\right) $
85944
Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $
35244
Prove $\sin^2\theta + \cos^2\theta = 1$
118884
The sine inequality $\frac2\pi x \le \sin x \le x$ for $0<x<\frac\pi2$
40537
How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$
107601
Use of inequality $1 - \cos (x) \leq x^2 /2$
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
105622
How to show $ \sin x \geq \frac{2x}{\pi}, x \in [0, \frac{\pi}{2}]$?
141787
Anybody know a proof of $\prod_{n=1}^\infty\cos(x/2^n)=\sin x/x$.
123476
Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$
23288
Prove that $x^2<\sin x \tan x$ as $x \to 0$
103757
how can I prove that $\frac{\arctan x}{x }< 1$?
123920
How prove this inequality $\tan{(\sin{x})}>\sin{(\tan{x})}$
115128
How do I show this $\cos^2(\arctan(x))=\frac{1}{1+x^2}$
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
7296
Prove $(1-\cos x)/\sin x = \tan x/2$