A) \[x+y+xy=1\]
B) \[x+y-xy=1\]
C) \[x+y+xy+1=0\]
D) \[~x+y-xy+1=0\]
Correct Answer: A
Solution :
Given that \[{{\tan }^{-1}}x\,{{\tan }^{-1}}y=\frac{\pi }{4}\] \[\Rightarrow \] \[{{\tan }^{-1}}\left( \frac{x+y}{1-xy} \right)=\frac{\pi }{4}\] \[\Rightarrow \] \[\frac{x+y}{1-xy}=\tan \frac{\pi }{4}=1\] \[\Rightarrow \] \[x+y=1-xy\] \[\Rightarrow \] \[x+y+xy=1\]
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