query: What is the value of $\cot70+4\cos70?$
positive_passages.docid: 74143
positive_passages.text: Simplifying and evaluating $\cot 70^\circ+4\cos 70^\circ$
negative_passages.docid: 100320
negative_passages.text: Prove that $\cos\frac {2\pi}{7}+ \cos\frac {4\pi}{7}+ \cos\frac {8\pi}{7}=-\frac{1}{2}$
negative_passages.docid: 5747
negative_passages.text: $\cos(\arcsin(x)) = \sqrt{1 - x^2}$. How?
negative_passages.docid: 17168
negative_passages.text: Find the value of $\sin\frac{2\pi}{7}+\sin\frac{4\pi}{7}+\sin\frac{8\pi}{7}$
negative_passages.docid: 153422
negative_passages.text: How to find the corrsponding expression after working with natural units $\hbar=c=1$?
negative_passages.docid: 30429
negative_passages.text: How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?
negative_passages.docid: 63679
negative_passages.text: Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?
negative_passages.docid: 104828
negative_passages.text: Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}...\cot \frac{(m-1)\pi}{2m}=1$
negative_passages.docid: 59791
negative_passages.text: Determine the exact value of equations involving more two trig variables
negative_passages.docid: 105117
negative_passages.text: $1 + \frac{1}{3}\frac{1}{4} + \frac{1}{5}\frac{1}{4^2} + \frac{1}{7}\frac{1}{4^3} + ..........$
negative_passages.docid: 81102
negative_passages.text: Cosine of the sum of two solutions of trigonometric equation $a\cos \theta + b\sin \theta = c$
negative_passages.docid: 148883
negative_passages.text: Sum of the series $\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\dots$
negative_passages.docid: 49443
negative_passages.text: What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$?
negative_passages.docid: 12414
negative_passages.text: prove that : $\cos x \cdot \cos(x-60^{\circ}) \cdot \cos(x+60^{\circ})= \frac14 \cos3x$
negative_passages.docid: 39752
negative_passages.text: Is there a limit of $\cos(n!)$?
negative_passages.docid: 116649
negative_passages.text: Value of: $ \frac {1} {\sqrt {4} + \sqrt {5}} + \frac {1} {\sqrt {5} + \sqrt {6}} + ... + \frac {1} {\sqrt {80} + \sqrt {81}}$
negative_passages.docid: 66872
negative_passages.text: Exact values of $\cos(2\pi/7)$ and $\sin(2\pi/7)$