If `0lexle1` then `tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-x^(2))/(1+x^(2)))}` is equal to

Options

A. `(2x)/(1-x^(2))`
B. 0
C. `(2x)/(1+x^(2))`
D. x

Answer

A

Explanation

We know that
`sin^(-1)(2x)/(1+x^(2))=2tan^(-1)xif -1 lexle1`
and
`cos^(-1)(1+x^(2))/(1+x^(2))=2tan^(-1)x if 0lexleinfty`
`therefore tan{1/2sin^(-1)(2x)/(1+x^(2))+1/2cos^(-1)(1-x^(2))/(1+x^(2))}`
`=tan(tan^(-1)(2x)/(1-x^(2)))=(2x)/(1-x^(2))`