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  4. The value of cos-1(cos (5π/3))+sin-1(sin (5π /3)) is

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

Inverse Trigonometric Functions

Solution:

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