`sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))]` is

Options

A. 1
B. `-1`
C. 0
D. none of these

Answer

A

Explanation

We know that
`tan^(-1)((2x)/(1-x^(2))=2 tan^(-1)x if -1 ltx le1`
and
`therefore sin{ tan^(-1)(1-x^(2))/(2x)+cos^(-1)(1-x^(2))/(1+x^(2))}`
`=sin{cot^(-1)(2x)/(1-x^(2))+cos^(-1)(1-x^(2))/(1+x^(2))`
`=sin{(pi)/(2)-2tan^(-1) x+2 tan^(-1)x} if 0 le x lt1`
`=sin(pi)/(2)=1`