Inverse sine sum formula for JEE

Formula

\(\sin^{-1}x+\sin^{-1}y=\sin^{-1}\left(x\sqrt{1-y^2}+y\sqrt{1-x^2}\right)\)

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

Conditions: Valid when the sum lies in \([-\pi/2,\pi/2]\); otherwise principal value adjustment required.

Advanced simplification and transformation of inverse-sine sums.