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