Step-by-step Solution:

Given that \(A-B=\frac{\pi}{4}\) \[\] \(\Rightarrow \tan (A-B)=\tan \frac{\pi}{4}\) \[\] \(\Rightarrow \frac{\tan A-\tan B}{1+\tan A \tan B}=1\) \[\] \(\Rightarrow \tan A-\tan B=1+\tan A \tan B\) \[\] \(\Rightarrow \tan A-\tan B-\tan A \tan B=1\) \[\] Adding 1 on both sides \[\] \((1+\tan A)-\tan B(1+\tan A)=2\) \[\] \((1+\tan A)(1-\tan B)=2\) \[\] Choice (A)\[\]