How can I prove that $\frac{\sin\theta+ \tan\theta}{2}> \theta$ when $0 < \theta < \frac{\pi}{2}$
51979
Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
98741
Finding $\int_{0}^{\frac{\pi}{4}} \frac{\tan \theta - \tan^3 \theta}{\ln \tan \theta}$
68881
Solve for $\theta$: $a = b\tan\theta - \frac{c}{\cos\theta}$
22709
Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.
75679
How to prove that $2 \arctan\sqrt{x} = \arcsin \frac{x-1}{x+1} + \frac{\pi}{2}$
122169
Prove $\sin(\pi/2)=1$ using Taylor series
17769
Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$
156881
How prove this inequality $I=\int_{0}^{\sqrt{2\pi}}\sin{x^2}dx>0$
121362
If $A,B>0$ and $A+B = \frac{\pi}{3},$ Then find Maximum value of $\tan A\cdot \tan B$.
10289
Need help in proving that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$
48586
Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
32823
Prove $\forall n \in \mathbb{N}: \int_{0}^{\frac{\pi}{2}} |\frac{\sin(nx)}{x}|dx \geq \frac{2}{\pi}\sum_{k=1}^{n}\frac{1}{k}$
1859
Proving $\arctan(\sqrt{x^2+1}-x)=\frac{\pi}{4}-\frac{1}{2}\arctan(x)$
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
32197
Prove that $\tan A + \tan B + \tan C = \tan A\tan B\tan C,$ $A+B+C = 180^\circ$
23288
Prove that $x^2<\sin x \tan x$ as $x \to 0$