query: Solve $\frac {2 \tan x}{1-\tan^2x} = \sin^22x$
positive_passages.docid: 147113
positive_passages.text: How to solve $2 \tan x / (1 - (\tan x)^2) = (\sin 2x)^2$?
negative_passages.docid: 31852
negative_passages.text: An elegant way to solve $\frac {\sqrt3 - 1}{\sin x} + \frac {\sqrt3 + 1}{\cos x} = 4\sqrt2 $
negative_passages.docid: 137376
negative_passages.text: Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$
negative_passages.docid: 85872
negative_passages.text: Prove $1 + \tan^2\theta = \sec^2\theta$
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: 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: 154219
negative_passages.text: Help with integral $\int\frac{1}{\sqrt{\tan x}}dx$
negative_passages.docid: 131688
negative_passages.text: Solve $\sin 7x+\sin 3x=0$
negative_passages.docid: 129880
negative_passages.text: Proving $\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$
negative_passages.docid: 23288
negative_passages.text: Prove that $x^2<\sin x \tan x$ as $x \to 0$
negative_passages.docid: 51729
negative_passages.text: Solve the following equation: $\sqrt {\sin x - \sqrt {\cos x + \sin x} } = \cos x$
negative_passages.docid: 65239
negative_passages.text: Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
negative_passages.docid: 47206
negative_passages.text: $-1 = 0$ by integration by parts of $\tan(x)$
negative_passages.docid: 97326
negative_passages.text: Find $\lim_{x \to 0} (\frac{\tan(x)}{x})^{\frac{1}{x}}$
negative_passages.docid: 131310
negative_passages.text: Evaluating $\dfrac{1}{\sin(2x)} + \dfrac{1}{\sin(4x)} + \dfrac{1}{\sin(8x)} + \dfrac{1}{\sin(16x)}$
negative_passages.docid: 45343
negative_passages.text: Solve $\cos^{n}x-\sin^{n}x=1$ with $n\in \mathbb{N}$.
negative_passages.docid: 122913
negative_passages.text: Evaluate $\int \frac{\sec^{2}{x}}{(\sec{x} + \tan{x})^{5/2}} \ \mathrm dx$