Question

`tan^-1  (1 - x)/(1 + x) = 1/2tan^-1x, (x > 0)`, x then will be equal to.

Options

• 1

• `sqrt(2)`

• `1/sqrt(3)`

• `1/sqrt(2)`

Answer 1

`1/sqrt(3)`

Explanation:

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

⇒ `tan^-1 1 - tan^-1x = 1/2 tan^-1x`

⇒ `pi/4 = 3/2 tan^-1x`

⇒ `tan^-1 x = pi/6`

∴ `x = 1/sqrt(3)`