How do I prove this trigonometric inequality?
42545
If $ a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}<1$
7966
How prove $ \sqrt{2}+\sqrt{3}>\pi$?
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
126032
Proving a certain inequality
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
141645
Trigonometric series sum proof
95633
Help with this trigonometry problem
15232
Proving an inequality involving real powers
2491
For $0 < x < \pi/2 $, prove that $x + \frac{x^{3}}{3} <\tan x $
48586
Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
114822
Prove or disprove an inequality involving complex numbers
60230
Prove that $\frac{1+\sin\theta+i\cos\theta}{1+\sin\theta-i\cos\theta}=\sin\theta+i\cos\theta$
77134
Proving a three variables inequality
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
137791
Proving inequality $\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq \sqrt{3 \left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)}$
58932
Hard contest type trigonometry proof
109171
How to evaluate this trigonometric limit?