Question

If `tan^(-1)  (x- 3)/(x - 4) + tan^(-1)  (x +3)/(x + 4) = pi/4`, then find the value of x.

Answer 1

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

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

`=> tan^(-1) [((x - 3)(x + 4)+(x+3)(x-4))/((x^2 - 16) - (x^2 - 9))] = pi/4`

`=> (x^2 + x - 12 + x^2 - x -12)/(x^2 -16 - x^2 +9) = tan pi/4`

`=> (2x^2 - 24)/-7 =  1`

2x² - 24 = -7

2x² = 17

`x^2 = +-sqrt(17/2)`