If `2tan^(-1)x+sin^(-1)(2x)/(1+x^2)` is independent of `x ,` then

Options

A. `x gt 1`
B. `x lt -1`
C. `0 lt x lt 1`
D. `-1 lt x lt 0`

Answer

A, B

Explanation

We know that
if `|x| le 1, " then " 2 tan^(-1) x = sin^(-1) ((2x)/(1 + x^(2)))`
if `x gt 1, " then " 2 tan^(-1) x = pi - sin^(-1) ((2x)/(1 + x^(2)))`
if `x lt -1, " then " 2 tan^(-1) x = - pi - sin^(-1) ((2x)/(1 + x^(2)))`
Hence, the required values are `x lt -1 " or " x gt 1`