If \(A-B=\frac{\pi}{4}\), then \((1+\tan A)(1-\tan B)\) is equal to
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)\[\]
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