Question

Find the principal value of the following:

tan⁻¹ (−1)

Answer 1

Let tan⁻¹ (−1) = y

Then tan y = −1 = `-tan (pi/2) = tan (-pi/2)`

We know that the range of the principal value branch of tan⁻¹ is `(-pi/2, pi/2)` and `tan(-pi/4) = - 1`.

Where `-pi/4 ∈ (-pi/2, pi/2)`

Therefore, the principal value of  tan⁻¹ (−1) is `pi/4`.