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INVERSE TRIGNOMETRIC FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINVERSE TRIGNOMETRIC FUNCTIONS1 Mark
Question
Evaluate the following:
$\tan^{-1}(\tan4)$
✓

Answer

We know that
$\tan^{-1}(\tan\theta)=\theta,-\frac{\pi}{2}<\theta<\frac{\pi}{2}$
We have
$\tan^{-1}(\tan4)$
$=4-\pi$ $\Big(\because\ \tan^{-1}(\tan\theta)=\theta-\pi,\text{if }\theta\in\Big(\frac{\pi}{2},\frac{3\pi}{2}\Big)\Big)$

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