Question

If $A+B={45}^{\circ },$ then $(1+\tan A)(1+\tan B)=$ $?$

Answer 1

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}=\tan \left({45}^{\circ }\right)=1$

$⟹\tan A+\tan B=1-\tan A\tan B$

$⟹\tan A(1+\tan B)+1(1+\tan B)=2$

$⟹(1+\tan A)(1+\tan B)=2$