Question

Find the principal value of the following:

`tan^-1(1/sqrt3)`

Answer 1

Let `tan^-1(1/sqrt3) = y`

Then,

`tany=1/sqrt3`

We know that the range of the principal value branch is `(-pi/2,pi/2)`.

Thus,

`tany=1/sqrt3=tan(pi/6)`

`=>y=pi/6in (-pi/2,pi/2)`

Hence, the principal value of `tan^-1(1/sqrt3)   is  pi/6`