Question

Find the principal value of the following:

tan^–1 (–1)

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`.

Where `-pi/4 ∈ (-pi/2, pi/2)`

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