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)` are `-sqrt(3)`.

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