query: Find $\sin^2x + \sin^2y + \sin^2z$, given $\tan^2x\tan^2y + \tan^2y\tan^2z + \tan^2z\tan^2x + 2\tan^2x\tan^2y\tan^2z = 1$
positive_passages.docid: 47356
positive_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: 111443
negative_passages.text: Optimization of $2x+3y+z$ under the constraint $x^2+ y^2+ z^2= 1$
negative_passages.docid: 118456
negative_passages.text: Find $\sum_{n=1}^{\infty}\tan^{-1}\frac{2}{n^2}$
negative_passages.docid: 16270
negative_passages.text: Trigonometry question: $\sin^2(A) + \sin^2(B) - \sin^2(C) = 2\sin(A)\sin(B)\cos(C).$
negative_passages.docid: 146594
negative_passages.text: Prove that $\frac{d}{dx}(\tan^{-1}(x))=\frac{1}{1+x^2}dx$
negative_passages.docid: 107067
negative_passages.text: Finding the argument of $z=1-\cos(2\theta)-i\sin(2\theta)$
negative_passages.docid: 70765
negative_passages.text: If $\frac{\tan(a+b-c)}{\tan(a-b+c)}=\frac{\tan c}{\tan b}$, then $\sin(b-c)=0$ or $\sin 2a + \sin2b + \sin 2c=0$
negative_passages.docid: 122705
negative_passages.text: Solution of trigonometric equation $0 = x\cos(x)+2$
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: 30600
negative_passages.text: Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$?
negative_passages.docid: 45343
negative_passages.text: Solve $\cos^{n}x-\sin^{n}x=1$ with $n\in \mathbb{N}$.
negative_passages.docid: 154216
negative_passages.text: Solve $\sin(z) = z$ in complex numbers
negative_passages.docid: 140983
negative_passages.text: $ \tan 1^\circ \cdot \tan 2^\circ \cdot \tan 3^\circ \cdots \tan 89^\circ$
negative_passages.docid: 12442
negative_passages.text: Solution of tanx = x?
negative_passages.docid: 117446
negative_passages.text: calculation of $\int_{0}^{1}\tan^{-1}(1-x+x^2)dx$
negative_passages.docid: 82016
negative_passages.text: Given $p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$, solve for $s$
negative_passages.docid: 84730
negative_passages.text: use the fact that $\tan 2x=\sin2x \ /\cos2x$ to prove that $\tan 2x=2\tan x/(1-\tan^2x)$