A) two
B) one
C) infinite
D) None of these
Correct Answer: A
Solution :
| \[{{\tan }^{-1}}x+{{\tan }^{-1}}\frac{1}{y}={{\tan }^{-1}}3\] |
| \[\Rightarrow \,\,{{\tan }^{-1}}\frac{x+\frac{1}{y}}{1-\frac{x}{y}}={{\tan }^{-1}}3\Rightarrow \frac{xy+1}{y-x}=3\] |
| \[\Rightarrow \,\,\,y=\frac{1+3x}{3-x}>0\] [\[\because \]x and y are positive] |
| \[\Rightarrow \,\,x-3<0\Rightarrow x<3\] or \[x=1,2\] |
| \[\therefore \,\,\,y=2,7\] solution set is \[(x,y)\,\,\in \left\{ (1,2),(2,7) \right\}\] |
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