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  4. The value of tan -1 tan ((3 π/5)) is

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

Inverse Trigonometric Functions

Solution:

We have, $\tan ^{-1}\left\{\tan \left(\frac{3 \pi}{5}\right)\right\}$
$=\tan ^{-1}\left\{\tan \left(\pi-\frac{2 \pi}{5}\right)\right\}=\tan ^{-1}\left\{\tan \left(\frac{-2 \pi}{5}\right)\right\}$
$=\frac{-2 \pi}{5} \left[\because \tan ^{-1}(\tan x)=x, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\right]$