Hint needed to show that $a\cos t+b\sin t\leq \sqrt{a^2+b^2}$ for $t\in [0,2\pi)$
45619
Prove: $|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$
52625
Prove inequality $\sqrt{\frac{2a}{b+a}} + \sqrt{\frac{2b}{c+b}} + \sqrt{\frac{2c}{a+c}} \leq 3$
77576
Using the triangle inequalities to prove a bound in the complex plane
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
157328
A complex analysis problem to prove an inequality
135895
Proving the bounds of cosine
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
145632
Proving $\frac{1}{\cos^2\alpha}<\frac{\tan\beta-\tan\alpha}{\beta-\alpha}<\frac{1}{\cos^2\beta}$
131754
Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $?
52413
Show that $\tan{(\pi/7)} \tan{(2\pi/7)}\tan{(3\pi/7)}=\sqrt{7}$
7966
How prove $ \sqrt{2}+\sqrt{3}>\pi$?
11711
Prove trigonometry identity for $\cos A+\cos B+\cos C$
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
107601
Use of inequality $1 - \cos (x) \leq x^2 /2$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
39266
Show that $\tan {\pi \over 8} = \sqrt 2 - 1$