Solve `Tan^(-1) - Tan^(-1) (X - Y)/(X+Y)` is Equal to - Mathematics

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

(A) `pi/2`

(B). `pi/3`

(C) `pi/4`

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

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`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.

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Chapter 2 Inverse Trigonometric Functions
Q 17 | Page 52