Question

Find the principal value of the following:

`cot^-1(sqrt3)`

Answer 1

Let `cot^-1(sqrt3)=y`

Then,

`coty=sqrt3`

We know that the range of the principal value branch is (0, π).

Thus,

`coty-sqrt3=cot(pi/6)`

`=>y=pi/6in(0,pi)`

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