The principal value of \( \cot ^{-1} x \) lies in the interval. (1)...

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The principal value of \( \cot ^{-1} x \) lies in the interval.
(1) \( (0, \pi) \)
(2) \( [0, \pi] \)
\( \mathrm{P} \)
(3) \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \)
(4) \( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
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