The sine inequality $\frac2\pi x \le \sin x \le x$ for $0<x<\frac\pi2$
11387
Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$
95266
Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
121548
proof of an inequality $ \left( 1+ \frac{x}{p} \right) ^{p}$
21088
Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
19167
Show that $X_{n}\sim N(\sin(\pi n),1)$ is uniformly tight
41293
Prove the inequalities $|z_1 +z_2| \geq \frac{1}{2}(|z_1|+|z_2|)|\frac {z_1} {|z_1|} +\frac {z_2} {|z_2|}|$
114822
Prove or disprove an inequality involving complex numbers
106803
How to see $\cos x \leq \exp(-x^2/2)$ on $x \in [0,\pi/2]$?
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
15237
Prove an inequality using complex analysis
1331
Approximation of the Sine function near $0$
115335
How can we prove this integral inequality?
117264
Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
35529
Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
30385
Proving that $\frac{e^x + e^{-x}}2 \le e^{x^2/2}$