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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Solution

(d) We know that, the principal value branch of $c o s e c^{- 1} i s [\frac{π}{2}, \frac{π}{2}] - [0] .$

$∴ y = c o s e c^{- 1} x$

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