Proof of $\sin(x) > \frac{2}{\pi} \cdot x $
118687
Prove an inequality with a $\sin$ function: $\sin(x) > \frac2\pi x$ for $0<x<\frac\pi2$
68774
Proving that $f(x)$ is less than or equal to $1+\pi/4$
44438
Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$
120795
Showing that $\sin^2x\cdot\sin^22x\cdot\sin^24x\cdot\sin^28x\cdots\sin^22^nx\leq\frac{3^n}{4^n}$
90573
Indefinite integral $\int(\sin x)^2/(x\cdot\cos x-\sin x)^2\,dx$
12414
prove that : $\cos x \cdot \cos(x-60^{\circ}) \cdot \cos(x+60^{\circ})= \frac14 \cos3x$
97253
How prove $e^x|f(x)|\le 2$ if $f(x)=\int_{x}^{x+1}\sin{(e^t)}dt$
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
148494
How does one prove that $\frac{1}{2}\cdot\frac{3}{4}\cdots \frac{2n-1}{2n}\leq \frac{1}{\sqrt{3n+1}}?$
150819
How to prove by induction that $|\sin(nx)| \leq n|\sin x|$?
35319
I'm looking for several ways to prove that $\int_{0}^{\infty }\sin(x)x^mdx=\cos(\frac{\pi m}{2})\Gamma (m+1)$
113080
Prove $\tan\big(\frac{\pi}{2} -\theta \big) = \cot \theta$
54638
Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
123920
How prove this inequality $\tan{(\sin{x})}>\sin{(\tan{x})}$
123136
Proof of the identity: $c\sin \frac{A-B}{2} \equiv (a-b) \cos \frac{C}{2}$
7296
Prove $(1-\cos x)/\sin x = \tan x/2$
51979
Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?