The principal value of \( \operatorname{cosec}^{-1} x \) lies in th...

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