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What is the principle value of "cosec"^(...

What is the principle value of `"cosec"^(-1)(-sqrt(2))` ?

A

`(pi)/(4)`

B

`(pi)/(2)`

C

`-(pi)/(4)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Let the principal value of `"cosec"^(-1)(-sqrt(2))=theta`
`rArr -sqrt(2)=cosec theta rArr -sqrt(2)=(1)/(sin theta)`
`rArr sin theta=-(1)/(sqrt(2))rArr theta =-(pi)/(4)`
Principal value of `"cosec"^(-1)(-sqrt(2))=-(pi)/(4)`
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