Which of the following is the principal value of ${cosec}^{- 1} x$

(- \frac{π}{2}, \frac{π}{2})

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(0, π) - {\frac{π}{2}}

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[- \frac{π}{2}, \frac{π}{2}]

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[- \frac{π}{2}, \frac{π}{2}] - {0}

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Solution

The correct option is D $[- \frac{π}{2}, \frac{π}{2}] - {0}$
We know that, the principal value of ${cosec}^{- 1} x$ is $[- \frac{π}{2}, \frac{π}{2}] - {0}$

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(- \frac{π}{2}, \frac{π}{2}) (b) [0, π] - \{\frac{π}{2}\} (c) [- \frac{π}{2}, \frac{π}{2}] (d) [- \frac{π}{2}, \frac{π}{2}] - \{0\}

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