Question

The value of $cos^{-1} \left(cos\frac{5\pi}{3}\right)+sin^{-1} \left(sin \frac{5\pi}{3}\right)$ is

Answer 1

$cos^{-1} \left(cos\frac{5\pi}{3}\right)+sin^{-1} \left(sin \frac{5\pi}{3}\right)$
$=cos^{-1} \left[cos \left(2\pi-\frac{\pi}{3}\right)\right]+sin^{-1}\left[sin \left(2\pi-\frac{\pi}{3}\right)\right]$
$=cos^{-1} \left[cos \frac{\pi}{3}\right]+sin^{-1} \left[sin \left(-\frac{\pi}{3}\right)\right]$
$=\frac{\pi}{3}+\left(-\frac{\pi}{3}\right)=0$