query: Find $x$ if $\frac1{\sin1°\sin2°}+\frac1{\sin2°\sin3°}+\cdots+\frac1{\sin89°\sin90°} = \cot x\cdot\csc x$
positive_passages.docid: 145500
positive_passages.text: Finite Series - reciprocals of sines
negative_passages.docid: 106544
negative_passages.text: Solve $ \frac{2}{\pi}\int_{-\pi}^\pi\frac{\sin\frac{9x}{2}}{\sin\frac{x}{2}}dx $
negative_passages.docid: 64255
negative_passages.text: Trigonometry problem
negative_passages.docid: 48586
negative_passages.text: Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
negative_passages.docid: 120797
negative_passages.text: Trigonometry question finding the sin and tan
negative_passages.docid: 12841
negative_passages.text: Ratio of sines given, find ratio of cosines?
negative_passages.docid: 51979
negative_passages.text: Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?
negative_passages.docid: 129319
negative_passages.text: Weird "hidden answer" in $2\tan(2x)=3\text{cot}(x)$
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: 617
negative_passages.text: Find θ: $β=\arctan\frac{(R+r)·\sin(θ)-r·\sin(θ(1+\frac{R}{r}))}{(R+r)·\cos(θ)-r·\cos(θ(1+\frac{R}{r}))}$
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: 7296
negative_passages.text: Prove $(1-\cos x)/\sin x = \tan x/2$
negative_passages.docid: 73538
negative_passages.text: solving $\cos z + \sin z = i$
negative_passages.docid: 50323
negative_passages.text: Find the general solution for this equation sin5θcos3θ = sin6θcos2θ.
negative_passages.docid: 84420
negative_passages.text: When is $\sin(x) = \cos(x)$?
negative_passages.docid: 60709
negative_passages.text: How do I get $\cos{\theta} \lt \frac{\sin{\theta}}{\theta} \lt 1$?
negative_passages.docid: 117331
negative_passages.text: Find the minimum value of $|\sin x+\cos x+\tan x+\cot x+\sec x+\csc x|$ for real numbers $x$