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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$\frac{\pi}{6}$

Vedclass · Answer

(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

Similar Questions

The principal value of $\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$ is

$2 \tanh^{-1} \frac{1}{2}$ is equal to

$\sin ^{-1}\left(-\frac{1}{2}\right)+\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)=$ . . . . . . .

Solve $\sin(\tan^{-1} x)$,where $|x| < 1$,is equal to:

Write $\cot ^{-1}\left(\frac{1}{\sqrt{x^{2}-1}}\right), x>1$ in the simplest form.

Vedclass Test Series

Exam Paper Generator

Online Exam Module