query: $\sin(\tan^{-1}(x/a)) = \frac{x/a}{\sqrt{1+(x/a)^2}}$
positive_passages.docid: 27132
positive_passages.text: Can't figure out how $\sin\left(\tan^{-1}(x)\right)=\frac{x}{\sqrt {x^2+1}}$
negative_passages.docid: 57152
negative_passages.text: Solve $\sin x = 1 - x$
negative_passages.docid: 85944
negative_passages.text: Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $
negative_passages.docid: 65239
negative_passages.text: Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
negative_passages.docid: 119815
negative_passages.text: Why is $\tan((1/2)\pi)$ undefined?
negative_passages.docid: 122169
negative_passages.text: Prove $\sin(\pi/2)=1$ using Taylor series
negative_passages.docid: 153867
negative_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
negative_passages.docid: 31379
negative_passages.text: Relationship between $\tanh x$ and $\arctan x$
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: 123920
negative_passages.text: How prove this inequality $\tan{(\sin{x})}>\sin{(\tan{x})}$
negative_passages.docid: 23288
negative_passages.text: Prove that $x^2<\sin x \tan x$ as $x \to 0$
negative_passages.docid: 12442
negative_passages.text: Solution of tanx = x?
negative_passages.docid: 111102
negative_passages.text: Prove the Trigonometric Identity: $\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}$
negative_passages.docid: 10289
negative_passages.text: Need help in proving that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$
negative_passages.docid: 29604
negative_passages.text: How to solve $\sin x +\cos x = 1$?
negative_passages.docid: 55436
negative_passages.text: Why does $A\sin{k(x+c)}=a\sin{kx}+b\cos{kx}$ imply that $A=\sqrt{a^2+b^2}$ and $\tan{c}=-b/a$?
negative_passages.docid: 42391
negative_passages.text: Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$