Aspire Faculty ID #3651 · Topic: NIMCET 2012 · Just now
NIMCET 2012

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

Solution

We know, $\tan(A-B)=\tan\frac{\pi}{4}=1$ 

Using the formula, 
$\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$ 
Therefore, $\frac{\tan A-\tan B}{1+\tan A\tan B}=1$ 
$\tan A-\tan B=1+\tan A\tan B$ 
Now, $(1+\tan A)(1-\tan B)$ 
$=1+\tan A-\tan B-\tan A\tan B$ 
$=1+(\tan A-\tan B)-\tan A\tan B$ 
$=1+(1+\tan A\tan B)-\tan A\tan B$ 
$=2$ 
Therefore, the correct answer is: 2
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