Find the value of, `cos [tan^(-1) {sin (cot^(-1)x)}]`

Options

A. `sqrt(x^(2)+2)/(x^(2)+3)`
B. `sqrt(x^(2)+2)/(x^(2)+1)`
C. `sqrt(x^(2)+1)/(x^(2)+2)`
D. none of these

Explanation

We have
`cos[tan^(-1) sin(cot(-1)x)]`
`cos{tan^(-1)(1)/sqrt(1+x^(2))}=sqrt(1+x^(2))/sqrt(2+x^(2))=sqrt(1+x^(2))=sqrt(1+x^(2))/(2+x^(2))`