Question

Simplify $\tan^{-1} ( \frac{x-\sqrt{1-x^2}}{x+\sqrt{1-x^2}} )$ with trigonometric substitution

score 199 · Answer 1 · 2026-03-28 03:27:26

199

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Simplify $\tan^{-1} ( \frac{x-\sqrt{1-x^2}}{x+\sqrt{1-x^2}} )$ with trigonometric substitution

Published on 28 Mar 2026 - 3:27

score 746 · Answer 2 · 2020-07-18 08:56:47

746

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score 145 · Answer 3 · 2020-07-22 04:19:48

145

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37

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256

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List Question

Simplify $\tan^{-1} ( \frac{x-\sqrt{1-x^2}}{x+\sqrt{1-x^2}} )$ with trigonometric substitution

Prove that $\tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac 12 \cos^{-1}x^2$

Definite integral using properties

Is a bijective smooth function a diffeomorphism almost everywhere?

Find inverse of cos function

Constructing an inverse of a composite function

Limits of inverse trigonometric fucnctions

A proof of the Continuity of the inverse matrix function

Inverting Laplace Transform with Geometric Series: $\mathcal{L}C(t) = \frac{\mu e^{-\beta \tau}}{1-\mu e^{-\beta \tau}}$

Evaluation of $\sum^{\infty} _{n=1} \arctan\left(\frac{4n}{n^4-2n^2+2}\right)$

Combinatorial problem on finding the index associated to an edge of a complete graph

Is Invariance of domain an overkill?

A Maclaurin expansion of $\arccos(-z)$ using only non-negative coefficients

basic function and relation concepts

What is $\csc^{-1}(\csc 0)$?

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