A) 1
B) \[\sqrt{3}\]
C) 2
D) \[\frac{1}{\sqrt{3}}\]
E) \[\frac{1}{2}\]
Correct Answer: C
Solution :
\[\therefore \] \[A+B=\frac{\pi }{4}\Rightarrow \tan (A+B)=1\] \[\Rightarrow \] \[\frac{\tan A+\tan B}{1-\tan A\tan B}=1\] \[\Rightarrow \] \[\tan A+\tan B+\tan A\tan B=1\] \[\Rightarrow \] \[(1+\tan A)(1+\tan B)=1+1=2\]You need to login to perform this action.
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