Question

Find the principal value of the following:

`cot^-1(-1/sqrt3)`

Answer 1

Let `cot^-1(-1/sqrt3)=y`

Then,

`coty=-1/sqrt3`

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

Thus,

`coty=-1/sqrt3=cot((2pi)/3)`

`=>y=(2pi)/3in(0,pi)`

Hence, the principal value of `cot^-1(-1/sqrt3)   is   (2pi)/3.`