Evaluate the following: ^ -1 ( 2) - Vidyadip

Question

Evaluate the following:
$\tan^{-1}(\tan2)$

✓

Answer

We know that
$\tan^{-1}(\tan\theta)=\theta,-\frac{\pi}{2}<\theta<\frac{\pi}{2}$
We have
$\tan^{-1}(\tan2)=\tan^{-1}[\tan(-\pi+2)]$
$=2-\pi$

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