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Q. Principal value of $\sec ^{-1}(2)$ is equal to

Inverse Trigonometric Functions

Solution:

Let $\sec ^{-1}(2)=\theta $
$\Rightarrow \sec \theta=2=\sec \frac{\pi}{3}$
$\Rightarrow \theta=\frac{\pi}{3} \in[0, \pi]-\left\{\frac{\pi}{2}\right\}$
$ \therefore $ Principal value of $\sec ^{-1}(2)$ is $\frac{\pi}{3}$