If `xgt0x,ygt0 and x gty` then `tan^(-1){(x)/(y)}+tan^(-1){(x+y)/(x-y)}` is equal to

Options

A. `(pi)/(4)`
B. `(pi)/(4)`
C. `(3pi)/(4)`
D. none of these

Answer

C

Explanation

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