Question
Evaluate the following:
$\tan^{-1}\Big(\tan\frac{7\pi}{6}\Big)$
$\tan^{-1}\Big(\tan\frac{7\pi}{6}\Big)$
✓
Answer
We know that $\tan^{-1}(\tan\theta)=\theta,-\frac{\pi}{2}<\theta<\frac{\pi}{2}$ We have$\tan^{-1}\Big(\tan\frac{7\pi}{6}\Big)=\tan^{-1}\Big[\tan\Big(\pi+\frac{\pi}{6}\Big)\Big]$
$=\tan^{-1}\Big[\tan\Big(\frac{\pi}{6}\Big)\Big]$ $=\frac{\pi}{6}$
$=\tan^{-1}\Big[\tan\Big(\frac{\pi}{6}\Big)\Big]$ $=\frac{\pi}{6}$
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