If A - B = 4 , then (1+ A )(1- B ) is equal to - Vidyadip

MCQ

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

✓
$2$
B
$0$
C
$1$
D
$3$

✓

Answer

Correct option: A.

$2$

$\tan (A-B)=\tan \frac{\pi}{4}$
$\Rightarrow \frac{\tan A-\tan B}{1+\tan A \tan B}=1$
$\Rightarrow \tan A=\tan B=1+\tan A \tan B \ldots (i)$
Now,
$=(1+\tan A)(1-\tan B)=1+\tan A=\tan B=\tan A \tan B$
$=1+1+\tan A \tan B=\tan A \tan B \text { (Using eq. (i)) }$
$=2$

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