Which of the following corresponds to the principal value branch

Question:

Which of the following corresponds to the principal value branch of $\tan ^{-1}$ ?

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

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

(c) $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\{0\}$

(d) $(0, \pi)$

Solution:

The principal value branch of $\tan ^{-1} x$ is $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.

Hence, the correct answer is option (a).

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