Answer
1
Work Step by Step
$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}=3$
$\implies \frac{\tan A+\frac{1}{2}}{1-\frac{1}{2}\tan A}=3$
Or $\tan A+\frac{1}{2}=3(1-\frac{1}{2}\tan A)$
$\implies \tan A+\frac{3}{2}\tan A=3-\frac{1}{2}$
$\implies \tan A(1+\frac{3}{2})=\frac{5}{2}$
Or $\tan A\times\frac{5}{2}=\frac{5}{2}$
$\implies \tan A=1$
