If `x gt y gt 0`, then find the value of `tan^(-1).(x)/(y) + tan^(-1) [(x + y)/(x -y)]`

Options

A. `(pi)/(2)`
B. `(pi)/(3)`
C. `(pi)/(4)`
D. `(pi)/(4) or -(3pi)/(4)`

Answer

C

Explanation

We have
`tan^(-1)(x/y)-tan^(-1)(x-y)/(x+y)`
`=tan^(-1)x/y-tan^(-1)(1-y//x)/(1+y//x)`
`=tan^(-1)x/y-(ta^(-1)1-tan^(-1)y/x)`
`tan^(-1)x/y+tan^(-1)y/x=(pi)/(4)=ta^(-1)x/y_+cot^(-1)x/y-(pi)/(2)-(pi)/(4)=(pi)/(4)`