Evaluate the following: ^ -1 ( 9 4 ) - Vidyadip

Question

Evaluate the following:
$\tan^{-1}\Big(\tan\frac{9\pi}{4}\Big)$

✓

Answer

We know that

$\tan^{-1}(\tan\theta)=\theta,-\frac{\pi}{2}<\theta<\frac{\pi}{2}$

We have

$\tan^{-1}\Big(\tan\frac{9\pi}{4}\Big)=\tan^{-1}\Big[\tan\Big(2\pi+\frac{\pi}{4}\Big)\Big]$

$\tan^{-1}\Big[\tan\Big(\frac{\pi}{4}\Big)\Big]$

$=\frac{\pi}{4}$

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