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Question
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Solution
Let `cot^-1(tan (3pi)/4) = y`
Then,
`coty=tan (3pi)/4`
We know that the range of the principal value branch is (0, π).
Thus,
`coty=tan (3pi)/4=-1=cot((3pi)/4)`
`=>y=(3pi)/4in(0,pi)`
Hence, the principal value of `cot^-1(tan (3pi)/4) is (3pi)/4.`
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