The range of the values of p for which the equation ` sin cos^(-1) ( cos (tan^(-1) x)) = p` has a solution is

Explanation

Range of `tan^-1x = [-pi/2,pi/2]`

Range of `cos(tan^-1x) = [0,1]`

Range of `cos^-1(cos(tan^-1x)) = [0,pi/2]`

Range of `sincos^-1(cos(tan^-1x)) = [0,1]`

`:.` Range of `p = [0,1]`


So, option `(b)` is the correct option.