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INVERSE TRIGNOMETRIC FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINVERSE TRIGNOMETRIC FUNCTIONS1 Mark
Question
Evaluate the following:
$\tan^{-1}\Big(\tan\frac{9\pi}{4}\Big)$
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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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