Question

If $A-B=\pi /4,$ then $(1+\tan A)(1-\tan B)$ is equal to?

• A. $2$
• B. $1$
• C. $0$
• D. $3$

Answer 1

Answer: (A)

$2$

Given $A-B=\frac{\pi }{4}$

$\tan (A-B)=\tan \frac{\pi }{4}$

$\frac{\tan A-\tan B}{1+\tan A\tan B}=1$

$⟹\tan A-\tan B=1+\tan A\tan B$

$⟹\tan A-\tan B-\tan A\tan B=1$

$⟹1+\tan A-\tan B(1+\tan A)=2$

$⟹(1+\tan A)(1-\tan B)=2$