Question:
If $A-B=\frac{\pi}{4}$, then $(1+\tan A)(1-\tan B)=$
Solution:
If $A-B=\frac{\pi}{4}$
then $(1+\tan A)(1-\tan B)=?$
Since $A-B=\frac{\pi}{4}$
i. e. $\tan (A-B)=\tan \frac{\pi}{4}$
i. e. $\frac{\tan A-\tan B}{1+\tan A+\tan B}=1$
i. e. $\tan A-\tan B=1+\tan A \tan B$
i. e. $\tan A-\tan B-\tan A \tan B=1$
i.e. $\tan A(1-\tan B)-\tan B+1=1+1 \quad$ (adding 1 both sides)
i. e. $(\tan A+1)(1-\tan B)=2$
i. e. value of $(1+\tan A)(1-\tan B)=2$
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