Question

Solve  `tan^(-1) -  tan^(-1)  (x - y)/(x+y)` is equal to

(A) `pi/2`

(B). `pi/3` 

(C) `pi/4` 

(D) `(-3pi)/4`

Answer 1

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

`= 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 `

Hence, the correct answer is C.