# How do you prove sin^-1(x)+cos^-1(x)=pi/2?

$L e t {\sin}^{-} 1 x = \theta \implies x = \sin \theta = \cos \left(\frac{\pi}{2} - \theta\right)$
$\implies {\cos}^{-} 1 x = \frac{\pi}{2} - \theta = \frac{\pi}{2} - {\sin}^{-} 1 x$
$\therefore {\sin}^{-} 1 x + {\cos}^{-} 1 x = \frac{\pi}{2}$