Prove that $\sin(a)$ + $\cos(a)\leq\sqrt{2}$
45619
Prove: $|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$
123920
How prove this inequality $\tan{(\sin{x})}>\sin{(\tan{x})}$
14386
Proof of an equality involving cosine $\sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{2}}}}\ =\ 2\cos (\pi/2^{n+1})$
11711
Prove trigonometry identity for $\cos A+\cos B+\cos C$
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
137791
Proving inequality $\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq \sqrt{3 \left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)}$
149447
Proving $\sin (x)=\cos (90^\circ-x)$
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
55436
Why does $A\sin{k(x+c)}=a\sin{kx}+b\cos{kx}$ imply that $A=\sqrt{a^2+b^2}$ and $\tan{c}=-b/a$?
152053
Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$
21941
Proving: $x = a_0 + \sum_{n=1}^{\infty}(a_n \cos nx + b_n \sin nx)$
49054
Show that $\left | \sin a - \sin b \right | \leq \left | a-b \right |$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
27911
How can I prove that $xy\leq x^2+y^2$?
42545
If $ a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}<1$
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$