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

MCQ

If $\text{A}-\text{B}=\frac\pi4,$ then $(1+\tan\text{A})(1-\tan\text{B})$ is equal to:

✓
$2$
B
$1$
C
$0$
D
$3$

✓

Answer

Correct option: A.

$2$

$\tan(\text{A - B})=\tan\frac\pi4$
$\Rightarrow\frac{\tan\text{A}-\tan\text{B}}{1+\tan\text{A}\tan\text{B}}=1$
$\Rightarrow\tan\text{A}-\tan\text{B}=1+\tan\text{A}\tan\text{B}\cdots(1)$
Now,
$(1+\tan\text{A})(1-\tan\text{B})=1+\tan\text{A}-\tan\text{B}-\tan\text{A}\tan\text{B}$
$=1+1+\tan\text{A}\tan\text{B}-\tan\text{A}\tan\text{B}$
$=2$

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