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If 2tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is ...

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

A

`x gt 1`

B

`x lt -1`

C

`0 lt x lt 1`

D

`-1 lt x lt 0`

Text Solution

Verified by Experts

The correct Answer is:
A, B
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`
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