If `(tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y`. Then which of the following may be true (A) `(x+y)/(tan1)=-2` (B) `(tan^(-1)x)/(1-tan^(-1)y)=2` (C) `(x+y)/(tan1)=2` (D) `(x+y)/(cot1)=1`

Options

A. `(x+y)/(tan1)=-2`
B. `(tan^(-1)x)/(1-tan^(-1)y)=2`
C. `(x+y)/(tan1)=2`
D. `(x+y)/(cot1)=1`

Answer

A

Explanation

`a^(3)+b^(3)+c^(3)=3abc`
`impliesa+b+c=0` or `a=b=c`
`impliestan^(-1)x+tan^(-1)y=1` or `tan^(-1)x=tan^(-1)y=-1`
`impliesx=y=-tan1` or `(x+y)/(1-xy)=tan1`
`(x+y)/(tan1)=-2`