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Question
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
Solution
Let `cot^-1(-1/sqrt3)=y`
Then,
`coty=-1/sqrt3`
We know that the range of the principal value branch is (0, π)
Thus,
`coty=-1/sqrt3=cot((2pi)/3)`
`=>y=(2pi)/3in(0,pi)`
Hence, the principal value of `cot^-1(-1/sqrt3) is (2pi)/3.`
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