The principal solution of ^ -1 ( (7 6 ) ) is

MCQ

The principal solution of $\tan ^{-1}\left(\tan \left(\frac{7 \pi}{6}\right)\right)$ is

A
$\frac{7 \pi}{6}$
B
$\frac{\pi}{6}$
C
$\frac{-\pi}{6}$
D
$\frac{-5 \pi}{6}$

✓

Answer

$
\begin{array}{l}
\text { (b) : In }\left(\frac{-\pi}{2}, \frac{\pi}{2}\right), \\
\tan ^{-1}\left(\tan \left(\frac{7 \pi}{6}\right)\right)=\tan ^{-1}\left(\tan \left(\pi+\frac{\pi}{6}\right)\right) \\
=\tan ^{-1}\left(\tan \left(\frac{\pi}{6}\right)\right)=\frac{\pi}{6}
\end{array}
$

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