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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:

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