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Find the principal value of sec^(-1)(...

Find the principal value of `sec^(-1)((-2)/(sqrt(3)))`

A

`pi/6`

B

`-pi/6`

C

`(5pi)/6`

D

`(7pi)/6`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `sec^(-1)(-2/sqrt(3))=x`, where `x in [0,pi]-{pi/2}`
Then, `secx=-2/sqrt(3)=-secpi/6 = sec(pi-pi/6)=sec(5pi)/6 rArr x=(5pi)/6`.
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