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