Question

If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______ 

Options

• `1/sqrt3`

• `sqrt3`

• 1

• -`sqrt3`

Answer 1

If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is `underline(1/sqrt3)`.

Explanation:

`tan^-1x = 2tan^-1((1 - x)/(1 + x))`

⇒ `1/2tan^-1x = tan^-1((1 - x)/(1 + (1)(x)))`

⇒ `1/2tan^-1 = tan^-1(1) - tan^-1x`

⇒ `1/2tan^-1x = pi/4 - tan^-1x`

⇒ `1/2tan^-1x + tan^-1x = pi/4` 

⇒ `tan^-1x = pi/6`

⇒ `x = tan  pi/6 = 1/sqrt3`