Question

If $A+B={45}^o$ Prove that: $(1+\tan A)(1+\tan B)=2$

Answer 1

$A+B={45}^o$

$\therefore \tan (A+B)=\tan {45}^o$

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

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

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

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

$=1+1$

$=2$