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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