query: Find the value of $\tan(x+100) = \tan(x+50)\tan(x)\tan(x-50)$
positive_passages.docid: 67710
positive_passages.text: Determine the smallest positive value of x(in degrees) for which: $\tan(x+100^{\circ}) = \tan(x+50^{\circ})\tan (x)\tan(x-50^{\circ})$
negative_passages.docid: 120797
negative_passages.text: Trigonometry question finding the sin and tan
negative_passages.docid: 88989
negative_passages.text: Why $x<\tan{x}$ while $0<x<\frac{\pi}{2}$?
negative_passages.docid: 31448
negative_passages.text: Calculate $\int\left( \sqrt{\tan x}+\sqrt{\cot x}\right)dx$
negative_passages.docid: 48956
negative_passages.text: Simplify $\arctan (\frac{1}{2}\tan (2A)) + \arctan (\cot (A)) + \arctan (\cot ^{3}(A)) $
negative_passages.docid: 105226
negative_passages.text: How to solve this equation manually: $(x^2+100)^2=(x^3-100)^3$?
negative_passages.docid: 2491
negative_passages.text: For $0 < x < \pi/2 $, prove that $x + \frac{x^{3}}{3} <\tan x $
negative_passages.docid: 25065
negative_passages.text: What is $\arctan(x) + \arctan(y)$
negative_passages.docid: 19791
negative_passages.text: Calculating $\lim_{x\to0} \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$
negative_passages.docid: 78448
negative_passages.text: Find the acute angle $x$ for $\tan x = \tan(x+10^\circ)\tan(x+20^\circ)\tan(x+30^\circ)$.
negative_passages.docid: 143368
negative_passages.text: Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$
negative_passages.docid: 83332
negative_passages.text: Trig sum: $\tan ^21^\circ+\tan ^22^\circ+\cdots+\tan^2 89^\circ = \text{?}$
negative_passages.docid: 17769
negative_passages.text: Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$
negative_passages.docid: 9539
negative_passages.text: $\alpha$ and $\beta$ are solution of $a \cdot \tan\theta + b \cdot \sec\theta = c$ show $ \tan(\alpha + \beta) = \frac{2ac}{a^2 - c^2}$
negative_passages.docid: 104384
negative_passages.text: Trigonometric identity: $\frac {\tan\theta}{1-\cot\theta}+\frac {\cot\theta}{1-\tan\theta} =1+\sec\theta\cdot\csc\theta$
negative_passages.docid: 47356
negative_passages.text: If : $\tan^2\alpha \tan^2\beta +\tan^2\beta \tan^2\gamma + \tan^2\gamma \tan^2\alpha + 2\tan^2\alpha \tan^2\beta \tan^2\gamma =1\dots$
negative_passages.docid: 97326
negative_passages.text: Find $\lim_{x \to 0} (\frac{\tan(x)}{x})^{\frac{1}{x}}$