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Question
What is the principal value of `cot^-1 ((-1)/sqrt(3))`?
Options
`pi/3`
`pi`
`(2pi)/3`
`2pi`
MCQ
Solution
`(2pi)/3`
Explanation:
Let `cot^-1 ((-1)/sqrt(3))` = y.
Then `cot y = (-1)/sqrt(3) = - cot(pi/3) = cot(pi - pi/3) = cot((2pi)/3)`
We know that the range of principle value branch of `cot^-1 (0, pi)` and `cot((2pi)/3) = (-1)/sqrt(3)`
Hence, principal value of `cot^-1 ((-1)/sqrt(3))` is `(2pi)/3`
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