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  4. The value of sec [ sin -1(- sin (50 π/9))+ cos -1 cos (-(31 π/9))] is equal to -

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Q. The value of $\sec \left[\sin ^{-1}\left(-\sin \frac{50 \pi}{9}\right)+\cos ^{-1} \cos \left(-\frac{31 \pi}{9}\right)\right]$ is equal to -

Inverse Trigonometric Functions

Solution:

$\sec \left[\sin ^{-1}\left(-\sin \frac{50 \pi}{9}\right)+\cos ^{-1} \cos \left(-\frac{31 \pi}{9}\right)\right]$
$=\sec \left[-\sin ^{-1}\left(\sin \frac{50 \pi}{9}\right)+\cos ^{-1} \cos \left(\frac{31 \pi}{9}\right)\right]$
$=\sec \left[-\sin ^{-1}\left(-\sin \frac{4 \pi}{9}\right)+\cos ^{-1}\left(-\cos \frac{4 \pi}{9}\right)\right]$
$=\sec \left[\frac{4 \pi}{9}+\pi-\frac{4 \pi}{9}\right]=\sec \pi=-1$