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

Question

Evaluate the following:
$\tan^{-1}(\tan1)$

✓

Answer

We know that

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

$\tan^{-1}(\tan1)$

$=1$ $\Big(\because\ \tan^{-1}(\tan\theta)=\theta,\text{if }\theta\in\Big(-\frac{\pi}{2},\frac{\pi}{2}\Big)\Big)$

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