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Question
Find the principal value of the following:
`cot^-1(-sqrt3)`
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Solution
Let `cot^-1(-sqrt3)` = y
Then,
cot y = `-sqrt3`
We know that the range of the principal value branch is (0, π)
Thus,
cot y = `-sqrt3 = cot((5pi)/6)`
`\implies` y = `(5pi)/6in(0, pi)`
Hence, the principal value of `cot^-1(-sqrt3)` is `(5pi)/6.`
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