Question

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

Answer 1

From given equation

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

⇒ `2[tan^-1 1 - tan^-1x] = tan^-1x`

⇒ `2(pi/4) = 3tan^-1x`

⇒ `pi/6 = tan^-1x`

⇒ x = `1/sqrt(3)`