Question

What is the principal value of `cot^-1 ((-1)/sqrt(3))`?

विकल्प

• `pi/3`

• `pi`

• `(2pi)/3`

• `2pi`

Answer 1

`(2pi)/3`

Explanation:

Let `cot^-1 ((-1)/sqrt(3))` = y.

Then `cot y = (-1)/sqrt(3) = - cot(pi/3) = cot(pi - pi/3) = cot((2pi)/3)`

We know that the range of principle value branch of `cot^-1 (0, pi)` and `cot((2pi)/3) = (-1)/sqrt(3)`

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