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).