Prove that $\tan\frac{\pi}{9}+ 4\sin\frac{\pi}{9}= \sqrt{3}$ .
12741
How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$
106544
Solve $ \frac{2}{\pi}\int_{-\pi}^\pi\frac{\sin\frac{9x}{2}}{\sin\frac{x}{2}}dx $
18285
Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
31852
An elegant way to solve $\frac {\sqrt3 - 1}{\sin x} + \frac {\sqrt3 + 1}{\cos x} = 4\sqrt2 $
15477
Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$?
22058
Prove that $\cos(\pi/7)$ is root of equation $8x^3-4x^2-4x+1=0$
108916
On the proof $\tan 70°-\tan 20° -2 \tan 40°=4\tan 10°$
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
85944
Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $
64497
prove that $\tan(\alpha+\beta) = 2ac/(a^2-c^2)$
70765
If $\frac{\tan(a+b-c)}{\tan(a-b+c)}=\frac{\tan c}{\tan b}$, then $\sin(b-c)=0$ or $\sin 2a + \sin2b + \sin 2c=0$
13297
Prove the following trigonometric identity without a calculator involved
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
30429
How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?
12414
prove that : $\cos x \cdot \cos(x-60^{\circ}) \cdot \cos(x+60^{\circ})= \frac14 \cos3x$
98741
Finding $\int_{0}^{\frac{\pi}{4}} \frac{\tan \theta - \tan^3 \theta}{\ln \tan \theta}$
7966
How prove $ \sqrt{2}+\sqrt{3}>\pi$?