Question

Find the principal value of the following:

`tan^(-1) (-sqrt3)`

Answer 1

Let `tan^(-1) (-sqrt(3)) = y`

Then, `tan y = -sqrt(3)`

= `-tan  pi/3`

= `tan (-pi/3)`

We know that the range of the principal value branch of tan⁻¹ x is `(-pi/2, pi/2)` and `tan(-pi/3)` is `-sqrt(3)`.

Therefore, the principal value of  `tan^(-1) (-sqrt3)` is `- pi/3`.