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  4. cos ( cos -1 cos ((8 π/7))+ tan -1 tan ((8 π/7))) has the value equal to

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Q. $\cos \left(\cos ^{-1} \cos \left(\frac{8 \pi}{7}\right)+\tan ^{-1} \tan \left(\frac{8 \pi}{7}\right)\right)$ has the value equal to

Inverse Trigonometric Functions

Solution:

$\cos ^{-1}\left(\cos \frac{8 \pi}{7}\right)=\cos ^{-1}\left(\cos \left(2 \pi-\frac{8 \pi}{7}\right)\right)=\cos ^{-1}\left(\cos \frac{6 \pi}{7}\right)=\frac{6 \pi}{7}$
$\tan ^{-1}\left(\tan \frac{8 \pi}{7}\right)=\tan ^{-1}\left(\tan \frac{\pi}{7}\right)=\frac{\pi}{7}$