Which of the following is the principal value branch of \( \operatorname{cosec}^{-1} x \) ? (A) ...

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Which of the following is the principal value branch of \( \operatorname{cosec}^{-1} x \) ?
(A) \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \)
(B) \( [0, \pi]-\left\{\frac{\pi}{2}\right\} \)
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(C) \( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
(D) \( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-\{0\} \)
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