Which of the following is the principle value branch of ${csc}^{- 1} x$ ?

(\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 C $(\frac{- π}{2}, \frac{π}{2}) - {0}$
We know that, the principle value branch of ${csc}^{- 1} x$ is $(\frac{- π}{2}, \frac{π}{2}) - {0}$

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{sec}^{- 1} x

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| z - 1 + i | + | z + i | = 1,

z

(

\in (- π, π])

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