Question

Solve the following equation: 

`tan^-1  (1 - x)/(1 + x) = 1/2 tan^-1x, (x > 0)`

Answer 1

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

⇒ `tan^-1 1 - tan^-1x = 1/2 tan^-1x`   ...`[tan^-1x - tan^-1y = tan^-1  (x - y)/(1 + xy)]`

⇒ `π/4 = 3/2 tan^-1x`

⇒ `tan^-1x = π/6`

⇒ `x = tan  π/6`

∴ `x = 1/sqrt(3)`