if $A + B = 45^0$ then the value of $(1 + tan A)(1 + tan B) =$ ??

2. Originally Posted by wizard654zzz
if $A + B = 45^0$ then the value of $(1 + tan A)(1 + tan B) =$ ??
hi

$A+B=45 so tan (A+B)=tan 45=1$

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

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

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

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