Question

Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$

score 10.1k · Answer 1 · 2026-03-17 08:14:12

Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$

score 45 · Answer 2 · 2026-03-20 03:27:12

45

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130

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List Question

Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$

Combination of functions and their inverses.

Solve $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ and avoid extra solutions while squaring

Find the greatest and least values of $(\sin^{-1}x)^2+(\cos^{-1}x)^2$

Is it always possible to rearrange an equation desirably?

Only bijective mappings are invertible. Clarifying proof.

Relating the roots of quadratic to an inverse trigonometric functions' question

Derive the conditions for $\tan^{-1}\frac{a\cos x-b\sin x}{b\cos x+a\sin x}=\tan^{-1}\frac{a}{b}-x$

Why is the inverse of the derivative of f not the actual derivative of the inverse of f?

$\ {\sin}^{-1}{(x)} $ equation and function

Check that the rotation isometry has an inverse

Is there a method to find inverse function of these specific polynomial?

solution to an Lagrangian Inverse Problem

Inverse trigonometric inequalities

Express $\cos(\tan^{-1}(x))$ in terms of $x$.

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