query: How to derive the formula for $\arctan(x) + \arctan(y)$ depending on $x,y$?
positive_passages.docid: 25065
positive_passages.text: What is $\arctan(x) + \arctan(y)$
negative_passages.docid: 61293
negative_passages.text: What's the derivative of: $ \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$?
negative_passages.docid: 24391
negative_passages.text: $\arcsin$ written as $\sin^{-1}(x)$
negative_passages.docid: 102496
negative_passages.text: Derivation of the formula for the vertex of a parabola
negative_passages.docid: 121057
negative_passages.text: Find a formula relating $\operatorname{arcsin}(x)$ and $\operatorname{arccos}⁡(x)$
negative_passages.docid: 85872
negative_passages.text: Prove $1 + \tan^2\theta = \sec^2\theta$
negative_passages.docid: 61343
negative_passages.text: Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
negative_passages.docid: 72157
negative_passages.text: Elementary proof of tangent half angle formula
negative_passages.docid: 24656
negative_passages.text: Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
negative_passages.docid: 120953
negative_passages.text: Show that, $2\arctan\left(\frac{1}{3}\right)+2\arcsin\left(\frac{1}{5\sqrt2}\right)-\arctan\left(\frac{1}{7}\right)=\frac{\pi}{4}$
negative_passages.docid: 23018
negative_passages.text: Integral $\int_a^\infty \frac{\arctan(x+b)}{x^2+c}dx$
negative_passages.docid: 64497
negative_passages.text: prove that $\tan(\alpha+\beta) = 2ac/(a^2-c^2)$
negative_passages.docid: 27127
negative_passages.text: Calculating $\iint (x+y) \, dx \, dy$
negative_passages.docid: 68116
negative_passages.text: How to derive this version of variance formula
negative_passages.docid: 60288
negative_passages.text: Why is $\arctan(x)=x-x^3/3+x^5/5-x^7/7+\dots$?
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: 69803
negative_passages.text: An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$