Question

If $A+B=\frac{\pi }{4}$, find the value of :

$(1+\tan A)(1+\tan B)$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

$A+B=\frac{\pi }{4}$

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

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

$\tan A+\tan B=1-\tan A\tan B$

$\tan A+\tan B+\tan A\tan B=1$

$1+\tan A+\tan B+\tan A\tan B=2$

$(1+\tan A)+\tan B(1+\tan A)=2$

$(1+\tan A)(1+\tan B)=2$