query: Value of $\tan(1^{\circ})+\tan(2^{\circ})+\tan(3^{\circ})+...+\tan(89^{\circ})$
positive_passages.docid: 95739
positive_passages.text: Sum of tangent functions where arguments are in specific arithmetic series
negative_passages.docid: 103144
negative_passages.text: Is there a way to write this expression differently: $\arctan 1/(1+n+n^2)$?
negative_passages.docid: 48956
negative_passages.text: Simplify $\arctan (\frac{1}{2}\tan (2A)) + \arctan (\cot (A)) + \arctan (\cot ^{3}(A)) $
negative_passages.docid: 84730
negative_passages.text: use the fact that $\tan 2x=\sin2x \ /\cos2x$ to prove that $\tan 2x=2\tan x/(1-\tan^2x)$
negative_passages.docid: 76941
negative_passages.text: How do you find the value of $\sum_{r=0}^{44} \tan^2(2r+1)$?
negative_passages.docid: 100907
negative_passages.text: $\sin\alpha + \sin\beta + \sin\gamma = 4\cos{\frac{\alpha}{2}}\cos{\frac{\beta}{2}}\cos{\frac{\gamma}{2}}$ when $\alpha + \beta + \gamma = \pi$
negative_passages.docid: 81727
negative_passages.text: How can I find the following product? $ \tan 20^\circ \cdot \tan 40^\circ \cdot \tan 80^\circ.$
negative_passages.docid: 25065
negative_passages.text: What is $\arctan(x) + \arctan(y)$
negative_passages.docid: 61343
negative_passages.text: Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
negative_passages.docid: 145632
negative_passages.text: Proving $\frac{1}{\cos^2\alpha}<\frac{\tan\beta-\tan\alpha}{\beta-\alpha}<\frac{1}{\cos^2\beta}$
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: 8919
negative_passages.text: If $\alpha = \frac{2\pi}{7}$ then the find the value of $\tan\alpha .\tan2\alpha +\tan2\alpha \tan4\alpha +\tan4\alpha \tan\alpha.$
negative_passages.docid: 147113
negative_passages.text: How to solve $2 \tan x / (1 - (\tan x)^2) = (\sin 2x)^2$?
negative_passages.docid: 109790
negative_passages.text: Finding the value of $\int_0^{\pi/2} \frac{dt}{1+(\tan(x))^{\sqrt{2}}}$
negative_passages.docid: 61119
negative_passages.text: Evaluate $\prod_{i=1}^{89} \sin (i)$
negative_passages.docid: 104272
negative_passages.text: Inequality of $\vert \text{tanh}(x)-x+\frac{x^3}{3}\vert\leq\frac{1}{8}$ for $x\in[-1/4,1/4]$
negative_passages.docid: 118456
negative_passages.text: Find $\sum_{n=1}^{\infty}\tan^{-1}\frac{2}{n^2}$