$(1+\tan 9°)(1+\tan 36°)=$

$\begin{array}{l}9°+36°=45°\\ \text{Apply} \tan \text{\hspace{0.17em}on both sides}\\ \tan (9°+36°)=\tan 45°\\ \frac{\tan 9°+\tan 36°}{1-\tan 9°\tan 36°}=1\\ \tan 9°+\tan 36°=1-\tan 9°\tan 36°\\ \tan 9°+\tan 36°+\tan 9°\tan 36°=1\\ \text{Adding} \text{'}1\text{'}\text{\hspace{0.17em}on both sides}\\ (1+\tan 9°)+\tan 36°(1+\tan 9°)=1+1\\ (1+\tan 9°)(1+\tan 36°)=2\end{array}$