If `cos^-1((x^2 -1)/(x^2+1))+ tan^-1 ((2x)/(x^2-1)) = (2pi)/3`, then x equal to (A) `sqrt(3)` (B) `2+sqrt(3)` (C) `2-sqrt(3)` (D) `-sqrt(3)`

Options

A. 2
B. `sqrt(3)`
C. 4
D. 3

Answer

B

Explanation

`cos^(-1)((x^(2)-1)/(x^(2)+1))=pi - co^(-1)((1-x^(2))/(1+x^(2)))=pi-2 tan^(-1)x` (as x gt 1)
`tan^(-1)((2x)/(x^(2)-1))=-tan^(-1)((2x)/(1-x^(2)))=pi-2 tan^(-1)x` (as x gt 1)
`therefore` Given equation is `2pi-4 tan^(-1)x = 2pi//3`
`therefore tan^(-1)x = pi//3`
`therefore x = sqrt(3)`