A) 1
B) 2
C) \[\infty \]
D) -2
Correct Answer: B
Solution :
Given that \[A+B=\frac{\pi }{4}\,\Rightarrow \,\tan \,(A+B)=\tan \,\frac{\pi }{4}\] \[\Rightarrow \,\,\frac{\tan A+\tan B}{1-\tan A\,\tan B}=1\] \[\Rightarrow \,\,\tan A+\tan B+\tan A\,\tan B=1\] \[\Rightarrow \,\,(1+\tan A)\,(1+\tan B)=2\].
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