Which of the following is the principal value branch of cosec^-1 ?
(a) $(- \frac{π}{2}, \frac{π}{2}) (b) [0, π] - \{\frac{π}{2}\} (c) [- \frac{π}{2}, \frac{π}{2}] (d) [- \frac{π}{2}, \frac{π}{2}] - \{0\}$

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Solution

The principal value branch of cosec⁻¹x is $[- \frac{π}{2}, \frac{π}{2}] - \{0\}$ .

Hence, the correct answer is option (d).

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Similar questions

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

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

f (x) = {sec}^{- 1} x

[π, \frac{3 π}{2}]

(\frac{π}{2}, π)

[- \frac{π}{2}, \frac{π}{2}]

[0, \frac{π}{2}]

Which of the following is the principal value branch of $c o s e c^{- 1} x ?$

(a) $(\frac{- π}{2}, \frac{π}{2})$ (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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