Question

Solve `tan^-1 2x + tan^-1 3x = pi/4`

Answer 1

Given tan^-1 (2x) + tan^-1 (3x) = `pi/4`

`tan^-1 [(2x + 3x)/(1 - (2x)(3x))] = pi/4`

`tan^-1 [(5x)/(1 - 6x^2)] = pi/4`

`(5x)/(1 - 6x^2) = tan  pi/4`

`(5x)/(1 - 6x^2)` = 1

⇒ 5x = 1(1 – 6x²)

⇒ 6x² + 5x – 1 = 0

⇒ (x + 1) (6x – 1) = 0

⇒ x + 1 = 0 (or) 6x – 1 = 0

⇒ x = -1 (or) x = `1/6`

x = -1 is rejected. It doesn’t satisfies the question.