Question

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

Answer 1

Given $A+B={45}^o$
{Take tan on both the sides }
$\tan (A+B)=\tan {45}^o$
or ,$\frac{\tan A+\tan B}{1-\tan A\tan B}=1$
or, $\tan A+\tan B=1-\tan A.\tan B$
or, $\tan A+\tan B+\tan A.\tan B=1$
Adding $"1"$ on both sides
or, $1+tanA+\tan B+\tan A.\tan B=1+1$
or, $(1+\tan A)+\tan B(1+\tan A).=2$
or, $(1+\tan A)(1+\tan B)=2$.