Question

The value of `tan^-1 (x/y) - tan^-1  (x - y)/(x + y)` is equal to

पर्याय

• `pi/4`

• `pi/2`

• `pi/3`

• `(- 3pi)/4`

Answer 1

`pi/4`

Explanation:

`tan^-1 (x/y) - tan^-1  (x - y)/(x + y) = tan^-1 [(x/y - (x - y)/(x + y))/(1 + (x/y)((x - y)/(x + y)))]`

= `tan^-1 [((x(x + y) - y(x - y))/(y(x - y)))/((y(x + y) - x(x - y))/(y(x - y)))]`

= `tan^-1 [(x^2 + xy - xy + y^2)/(xy + y^2 + x^2 - xy)]`

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