Inverse sine and inverse cosine in terms of inverse tangent for JEE

Formula

\(\sin^{-1}x=\tan^{-1}\left(\dfrac{x}{\sqrt{1-x^2}}\right),\quad \cos^{-1}x=\tan^{-1}\left(\dfrac{\sqrt{1-x^2}}{x}\right)\)

Variables: \(x\in[-1,1]\).

Conditions: For second formula, principal value depends on sign of \(x\); if \(x<0\), adjustment by \(\pi\) may be needed.

Interconversion among inverse trigonometric functions.