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

Explanation

We know, `-pi/2 lt tan^-1x lt pi/2`

`:. 0 lt cos(tan^-1x) le 1`

So, ` 0 le cos^-1(cos(tan^-1x)) lt pi/2`

` 0 le sin(cos^-1(cos(tan^-1x))) lt 1`

So, range of given expression is `[0,1)`.