Answer 1

Let tan⁻¹ (−1) = y. Then tan y = -1 = `-tan (pi/4) = tan (-pi/4)`

We know that the range of the principal value branch of tan⁻¹ is

`(-pi/2, pi/2) and  tan(-pi/4) = - 1`

Therefore, the principal value of  `tan^(-1) (-1) " is " pi/4`