The value of tan ^{-1}left(tan frac{7 pi}{6}r | vedclass

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(B) We know that the principal value branch of $	an ^{-1} x$ is $(-\frac{\pi}{2}, \frac{\pi}{2})$.Since $\frac{7 \pi}{6}$ does not lie in this interv

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$\frac{\pi}{6}$

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(B) We know that the principal value branch of $	an ^{-1} x$ is $(-\frac{\pi}{2}, \frac{\pi}{2})$.Since $\frac{7 \pi}{6}$ does not lie in this interval,we simplify the expression:$	an ^{-1}\left(	an \frac{7 \pi}{6}ight) = 	an ^{-1}\left(	an (\pi + \frac{\pi}{6})ight)$Using the identity $	an (\pi + 	heta) = 	an 	heta$,we get:$= 	an ^{-1}\left(	an \frac{\pi}{6}ight)$Since $\frac{\pi}{6} \in (-\frac{\pi}{2}, \frac{\pi}{2})$,the expression simplifies to:$= \frac{\pi}{6}$

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

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