query: Prove that $\tan \left(\frac{3\pi}{11}\right)+4\sin \left(\frac{2\pi}{11}\right)=\sqrt {11}$
positive_passages.docid: 12741
positive_passages.text: How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$
negative_passages.docid: 147684
negative_passages.text: Prove that $\sin \theta=\frac{3 \sin \alpha+\sin^3 \alpha}{1+3\sin^2 \alpha}$ using given condition
negative_passages.docid: 49109
negative_passages.text: Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
negative_passages.docid: 34905
negative_passages.text: Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$
negative_passages.docid: 123136
negative_passages.text: Proof of the identity: $c\sin \frac{A-B}{2} \equiv (a-b) \cos \frac{C}{2}$
negative_passages.docid: 104658
negative_passages.text: proving $\csc^2 \left( \frac{\pi}{7}\right)+\csc^2 \left( \frac{2\pi}{7}\right)+\csc^2 \left( \frac{4\pi}{7}\right)=8$
negative_passages.docid: 31448
negative_passages.text: Calculate $\int\left( \sqrt{\tan x}+\sqrt{\cot x}\right)dx$
negative_passages.docid: 2676
negative_passages.text: Finding $\frac {d(\tan \theta)}{d\theta}$
negative_passages.docid: 111102
negative_passages.text: Prove the Trigonometric Identity: $\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}$
negative_passages.docid: 34017
negative_passages.text: Show that $n^{\pi\left(2n\right)-\pi\left(n\right)}2$
negative_passages.docid: 42545
negative_passages.text: If $ a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}<1$
negative_passages.docid: 24656
negative_passages.text: Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
negative_passages.docid: 55779
negative_passages.text: How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?
negative_passages.docid: 82170
negative_passages.text: Solve $x = \frac{1}{2}\tan(x)$
negative_passages.docid: 132065
negative_passages.text: Prove sum of $\cos(\pi/11)+\cos(3\pi/11)+...+\cos(9\pi/11)=1/2$ using Euler's formula
negative_passages.docid: 21855
negative_passages.text: Prove $\sum_{n=1}^{\infty}\arctan{\left(\frac{1}{n^2+1}\right)}=\arctan{\left(\tan\left(\pi\sqrt{\frac{\sqrt{2}-1}{2}}\right)\cdots\right)}$
negative_passages.docid: 11059
negative_passages.text: Verify the identity: $\tan^{-1} x +\tan^{-1} (1/x) = \pi /2$