Showing that $0 < \cos (\theta)<\frac {\sin (\theta)}{\theta}<\frac {1}{\cos(\theta)} $
106828
If $0 \lt x \lt \frac{\pi}{2}$, is $\cos(x) \le \frac{\sin(x)}{x} \le \frac{1}{\cos(x)}$?
98745
To prove $(\sin\theta + \csc\theta)^2 + (\cos\theta +\sec\theta)^2 \ge 9$
105238
Proving $\tan(\theta_1+\theta_2+\cdots+\theta_n)$ has the form $\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$
128415
Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots+\frac{1}{3001}<\frac43$
23288
Prove that $x^2<\sin x \tan x$ as $x \to 0$
125088
show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
65562
Proving the inequality $\arctan\frac{\pi}{2}\ge1$
6100
Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$
55869
Use the Maclaurin series to prove that $e^{i\theta} = cos(\theta) + isin(\theta)$
113080
Prove $\tan\big(\frac{\pi}{2} -\theta \big) = \cot \theta$
126236
General closed form of $\int_{0}^{\theta_0} \frac{1}{\sqrt{\cos \theta-\cos \theta_0}} d\theta$
107067
Finding the argument of $z=1-\cos(2\theta)-i\sin(2\theta)$
17769
Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$