If `3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1,` then `x` is equal to (a)`1/(sqrt(3))` (b) `-1/(sqrt(3))` (c) `sqrt(3)` (d) `-(sqrt(3))/4`

Options

A. `(1)/(sqrt3)`
B. `-(1)/(sqrt3)`
C. `sqrt3`
D. `-(sqrt3)/(4)`

Answer

A

Explanation

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)`