Question

How do you find the exact value of `cot^-1(cot((2pi)/3))`?

Answer 1

`cot^-1(cot ((2pi)/3)) = ((2pi)/3)`

Explanation:

Let `cot^-1(cot ((2pi)/3)) = theta` , then

`cot theta = cot ((2pi)/3) :. theta = ((2pi)/3) :.`

`cot^-1(cot ((2pi)/3)) = ((2pi)/3)` [Ans]

Answer 2

Assuming `color(blue)(cot^-1)` is defined as a function with a range of `color(blue)([0,pi))`
then `cot^-1(cot((2pi)/3))=color(red)((2pi)/3)`