Prove that $\tan x \geq x + \frac{x^3}{3}$ for $x \in [0, \frac{\pi}{2})$
2491
For $0 < x < \pi/2 $, prove that $x + \frac{x^{3}}{3} <\tan x $
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
77978
Show that $\frac {\sin x} {\cos 3x} + \frac {\sin 3x} {\cos 9x} + \frac {\sin 9x} {\cos 27x} = \frac 12 (\tan 27x - \tan x)$
46353
Proof that $\cos(\pi/3)=1/2$
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
98741
Finding $\int_{0}^{\frac{\pi}{4}} \frac{\tan \theta - \tan^3 \theta}{\ln \tan \theta}$
65562
Proving the inequality $\arctan\frac{\pi}{2}\ge1$
32823
Prove $\forall n \in \mathbb{N}: \int_{0}^{\frac{\pi}{2}} |\frac{\sin(nx)}{x}|dx \geq \frac{2}{\pi}\sum_{k=1}^{n}\frac{1}{k}$
123920
How prove this inequality $\tan{(\sin{x})}>\sin{(\tan{x})}$
34349
Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$
90218
Proving $\frac{x}{y} +\frac{y}{z} + \frac{z}{x} \ge 3$ for positive $x,y,z$
30688
Prove that $\frac{x_1}{1+x_2+x_3+\ldots+x_n}+\frac{x_2}{1+x_1+x_3+\ldots+x_n}+\ldots+\frac{x_n}{1+x_1+x_2+\ldots+x_{n-1}}\ge\frac{n}{2n-1}$.
127759
Prove that $\frac{\sin(a)}{\sin(b)} < \frac{a}{b} < \frac{\tan(a)}{\tan(b)}$ where $0 < b < a < \frac{\pi}{2}$
89265
Proving that $x - \frac{x^3}{3!} 0$
104498
Show that $x^3y^3(x^3+y^3) \leq 2$
44705
Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
82321
Is $\cos(x) \geq 1 - \frac{x^2}{2}$ for all $x$ in $R$?