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