Question

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

Answer 1

Answer: 0

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