What is the principal value of `cos^(-1)cos((2pi)/3)+sin^(-1)sin((2pi)/3)?`

Explanation

`cos^-1cos((2pi)/3)+sin^-1sin((2pi)/3)`

We know, principal value of `cos^-1` is between `0` to `2pi` and for `sin^-1` is `-pi/2` to `pi/2`.

`:.` Principal value of `cos^-1cos((2pi)/3) = (2pi)/3`

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

`:.` Principal value of `sin^-1sin((2pi)/3) = pi/3`

`:.` Principal value of given expression ` = (2pi)/3+pi/3 = pi`