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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
Question
Evaluate the following:
$\tan^{-1}(\tan12)$
✓

Answer

We know that
$\tan^{-1}(\tan\theta)=\theta,-\frac{\pi}{2}<\theta<\frac{\pi}{2}$
We have
$\tan^{-1}(\tan12)$
$=12-4\pi$ $\Big(\because\ \tan^{-1}(\tan\theta)=\theta-4\pi,\text{if }\theta\in\Big(\frac{7\pi}{2},\frac{9\pi}{2}\Big)\Big)$

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