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Given that , tan^(-1) ((2x)/(1-x^(2)))...

Given that ,
`tan^(-1) ((2x)/(1-x^(2))) = {{:(2 tan^(-1) x"," |x| le 1),(-pi +2 tan^(-1)x","x gt 1),(pi+2 tan^(-1)x"," x lt -1):}`
`sin^(-1)((2x)/(1+x^(2))) ={{:(2 tan^(-1)x","|x|le1),(pi -2 tan^(-1)x","x gt 1 and ),(-(pi+2tan^(-1))","x lt -1):}`
`sin^(-1) x + cos^(-1) x = pi//2 " for " - 1 le x le 1`
`sin^(-1) ((4x)/(x^(2)+4)) + 2 tan^(-1)( - x/2)` is independent of x, then

A

`x in [-3,4]`

B

`x in [-2,2]`

C

`x in [-1,1]`

D

`x in [1,infty)`

Text Solution

Verified by Experts

The correct Answer is:
B
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