Question

Find the principal value of the following:

`cot^(-1) (sqrt(3))`

Answer 1

Let `cot^(-1) (sqrt(3)) = y`.

Then, `cot y = sqrt(3) = cot (pi/6)`.

We know that the range of the principal value branch of cot⁻¹ is (0, π) and `cot (pi/6) = sqrt(3)`.

Where `pi/6 ∈ (0, pi)`

Therefore, the principal value of `cot^(-1) (sqrt(3))` is `pi/6`.