Question

tan^-1 2x+tan^-1 3x=π÷4

Answer 1

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

tan^-1{ (2x + 3x ) / ( 1 - 6x2) } = pi / 4

5x / (1-6x2) = tan^-1pi/4 = 1

5x = 1 - 6x​^2

6x^2+ 5x - 1 = 0

6x^2+ 3x + 2x - 1 = 0

3x ( 2x + 1 ) + ( 2x - 1 ) = 0

(3x + 1) (2x - 1) =0

therefore, x = -1/3 or x = 1/2

@skb