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Question
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
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Solution
Let `sec^-1(2sin (3pi)/4)=y`
Then,
`secy=2sin (3pi)/4`
We know that the range of the principal value branch is `[0,pi]-{pi/2}.`
Thus,
`secy=2sin (3pi)/4=2xx1/sqrt2=sqrt2=sec(pi/4)`
`=>y=pi/4in[0,pi]`
Hence, the principal value of `sec^-1(2sin (3pi)/4) is pi/4`
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