Let $A, B$ and $C$ be the angles of an acute triangle. Show that: $\sin A+\sin B +\sin C > 2$.
96065
Question about sines of angles in an acute triangle
147886
Proof of the angle sum identity for $\sin$
45619
Prove: $|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$
56059
If $\frac{\sin^4 x}{a}+\frac{\cos^4 x}{b}=\frac{1}{a+b}$, then show that $\frac{\sin^6 x}{a^2}+\frac{\cos^6 x}{b^2}=\frac{1}{(a+b)^2}$
81102
Cosine of the sum of two solutions of trigonometric equation $a\cos \theta + b\sin \theta = c$
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
40952
Showing that sum of angles of hyperbolic triangle is strictly less than $\pi$
123133
If, in a triangle, $\cos(A) + \cos(B) + 2\cos(C) = 2$ prove that the sides of the triangle are in AP
139065
Proving $\csc\frac\alpha2+\csc\frac\beta2+\csc\frac\gamma2 \ge 6$, where $\alpha$, $\beta$, $\gamma$ are the angles of a triangle
22237
Proof of triangle inequality
12646
In acute angle triangle, prove that $\cos (A-B) \cos (B-C) \cos (C-A)\ge 8\cos A \cos B \cos C$
94091
In $ \triangle ABC$ show that $ 1 \lt \cos A + \cos B + \cos C \le \frac 32$
109133
$a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$
78448
Find the acute angle $x$ for $\tan x = \tan(x+10^\circ)\tan(x+20^\circ)\tan(x+30^\circ)$.
80095
Show $|a|+|b|+|c|+|a+b+c| \geq  |a+b|+|b+c|+|c+a|$ for complex $a$, $b$, $c$
148744
Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$
123136
Proof of the identity: $c\sin \frac{A-B}{2} \equiv (a-b) \cos \frac{C}{2}$