query: How to prove the trigonometric equality $\tan(\pi/7) \tan(2\pi/7) \tan(3\pi/7)= \sqrt 7$?
positive_passages.docid: 145559
positive_passages.text: Trigonometry problem on product of trig functions.
negative_passages.docid: 30600
negative_passages.text: Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$?
negative_passages.docid: 7296
negative_passages.text: Prove $(1-\cos x)/\sin x = \tan x/2$
negative_passages.docid: 56934
negative_passages.text: How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ ?.
negative_passages.docid: 79685
negative_passages.text: For natural $n$, prove $\prod_{k=1}^n \tan\left(\frac{k\pi}{2n+1}\right) = 2^n \prod_{k=1}^n \sin\left(\frac{k\pi}{2n+1}\right)=\sqrt{2n+1}$
negative_passages.docid: 13297
negative_passages.text: Prove the following trigonometric identity without a calculator involved
negative_passages.docid: 63679
negative_passages.text: Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?
negative_passages.docid: 51979
negative_passages.text: Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?
negative_passages.docid: 154172
negative_passages.text: Finding $\tan t$ if $t=\sum\tan^{-1}(1/2t^2)$
negative_passages.docid: 31379
negative_passages.text: Relationship between $\tanh x$ and $\arctan x$
negative_passages.docid: 137376
negative_passages.text: Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$
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: 113080
negative_passages.text: Prove $\tan\big(\frac{\pi}{2} -\theta \big) = \cot \theta$
negative_passages.docid: 42391
negative_passages.text: Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$
negative_passages.docid: 76490
negative_passages.text: Proving that $\cos(\arcsin(x))=\sqrt{1-x^2}$
negative_passages.docid: 120444
negative_passages.text: Trigonometric Triangle Equality
negative_passages.docid: 78528
negative_passages.text: Trigonometric fraction Inequality question