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If 3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)...

If `3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)((2x)/(1-x^2))=pi/3` , then `x` is equal to

A

`(1)/(sqrt3)`

B

`-(1)/(sqrt3)`

C

`sqrt3`

D

`-(sqrt3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
The given equation is
`3 (2 tan^(-1) x) -4 (2 tan^(-1) x) - 4 (2 tan^(-1) x) + 2(2 tan^(-1) x) = pi//3`
`:. 2 tan^(-1) x = pi//3`
`:. Tan^(-1) x = pi//6`
`:. X = (1)/(sqrt3)`
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