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

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

$A$ value of $x$ for which $\sin(\cot^{-1}(1 + x)) = \cos(\tan^{-1}x)$ is

If $y = \sin^{-1}\left(\frac{2^{x+1}}{1+4^x}\right)$ and $\frac{dy}{dx} = \frac{2^{x+1} \log 2}{f(x)}$,then $f(0) = $ . . . . . .

If the range of $\operatorname{sech}^{-1} x + \operatorname{cosech}^{-1} x$ is $[a, b]$,then

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module