Question

Find the principal value of the following:

`cot^(-1) (sqrt3)`

Answer 1

Let `cot^(-1) (sqrt3)` = y

 Then cot y = `sqrt3 = cot (pi/6)`

We know that the range of the principal value branch of cot⁻¹ is (0, π). 

Then `cot (pi/6) = sqrt3`

Where `pi/6 ∈ (0, pi)`

Therefore, the principal value of `cot^(-1) (sqrt3)` is `pi/6`.