The number of integral values of x satisfying the equation `tan^(-1) (3x) + tan^(-1) (5x) = tan^(-1) (7x) + tan^(-1) (2x)` is ____

Answer

1

Explanation

`tan^(-1) (3x) + tan^(-1) (5x) = tan^(-1) (7x) + tan^(-1) (2x)`
or `tan^(-1) (3x) - tan^(-1) (2x) = tan^(-1) (7x) - tan^(-1) (5x)`
or `tan^(-1) ((3x -2x)/(1 + 6x^(2))) = tan^(-1) ((7x -5x)/(1 + 35x^(2)))`
or `(x)/(1 + 6x^(2)) = (2x)/(1 + 25 x^(2))`
`rArr x = 0 " or " 1 + 35x^(2) = 2 + 12 x^(2)`
`rArr x = 0 " or " x = (1)/(sqrt23) "or " -(1)/(sqrt23)`