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Question
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
Solution
Let `\text(cosec)^-1(2/sqrt3)=y`
Then,
`\text(cosec) y=2/sqrt3`
We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}`
Thus,
`\text(cosec) y=2/sqrt3=text(cosec)(pi/3)`
`=>y=pi/3in[-pi/2,pi/2],y!=0`
Hence, the principal value of `\text(cosec)^-1(2/sqrt3) is pi/3`
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