# The principal value branch

Question:

The principal value branch of $\sec ^{-1}$ is

(a) $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$

(b) $[0, \pi]-\left\{\frac{\pi}{2}\right\}$

(c) $(0, \pi)$

(d) $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

Solution:

The principal value branch of $\sec ^{-1} x$ is $[0, \pi]-\left\{\frac{\pi}{2}\right\}$.

Hence, the correct answer is option (b).