Prove that 2/π ≤(sinx)/x ≤ 1 for all |x|≤ π/2.
11387
Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
148451
Polynomial inequality proof
124208
Proof $|\sin(x) - x| \le \frac{1}{3.2}|x|^3$
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
105622
How to show $ \sin x \geq \frac{2x}{\pi}, x \in [0, \frac{\pi}{2}]$?
146180
Prove that $x\sqrt{1-x^2} \leq \sin x \leq x$
122169
Prove $\sin(\pi/2)=1$ using Taylor series
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
49054
Show that $\left | \sin a - \sin b \right | \leq \left | a-b \right |$
30897
$\pi(x)\geqslant\frac{\log x}{2\log2}$ for all $x\geqslant2.$
45619
Prove: $|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$
105487
Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$
46353
Proof that $\cos(\pi/3)=1/2$
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
81618
Prove $||a|-|b| | \leq |a-b|$
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$