Question

Find the principal value of the following:

`cot^-1(-sqrt3)`

Answer 1

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.`