Find the principal value of sec ^{-1}left(fra | vedclass

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

Question

(A) Let $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right) = y$. Then,$\sec y = \frac{2}{\sqrt{3}}$. We know that $\sec \left(\frac{\pi}{6}\right) = \frac{2}{

Vedclass · Accepted Answer

$\frac{\pi}{6}$

Vedclass · Answer

(A) Let $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right) = y$. Then,$\sec y = \frac{2}{\sqrt{3}}$. We know that $\sec \left(\frac{\pi}{6}\right) = \frac{2}{\sqrt{3}}$. The range of the principal value branch of $\sec ^{-1}$ is $[0, \pi] - \{\frac{\pi}{2}\}$. Since $\frac{\pi}{6} \in [0, \pi] - \{\frac{\pi}{2}\}$,the principal value of $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)$ is $\frac{\pi}{6}$.

Find the principal value of $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)$

Similar Questions

If $\sin \left(\cot ^{-1}(x+1)\right)=\cos \left(\tan ^{-1} x\right)$,then considering positive square roots,$x$ has the value $\qquad$

The value of $\tan \left( \frac{1}{2} \cos^{-1} \left( \frac{\sqrt{5}}{3} \right) \right)$ is

If $\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,then $\cos^{-1}(\sin \theta)$ is equal to

The value of $\sin \left(2 \sin ^{-1} 0.8\right)$ is equal to

If $\tan \theta = - \frac{1}{\sqrt{3}}$,$\sin \theta = \frac{1}{2}$,and $\cos \theta = - \frac{\sqrt{3}}{2}$,then the principal value of $\theta$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module