(1+tg8)(1+tg9)(1+tg36)(1+tg37) = ?

Подготовительная работа:
$1)\ tg36= tg(45-9)=\frac{tg45-tg9}{1+tg45tg9} = \frac{1-tg9}{1+tg9} \\ 2)\ tg37= tg(45-8)=\frac{tg45-tg8}{1+tg45tg8} = \frac{1-tg8}{1+tg8}$
(1+tg8)(1+tg9)(1+tg36)(1+tg37) =
$=(1+tg8)(1+\frac{1-tg8}{1+tg8} )(1+tg9)(1+\frac{1-tg9}{1+tg9} )=\\ =(1+tg8)*\frac{1+tg8+1-tg8}{1+tg8} *(1+tg9)*\frac{1+tg9+1-tg9}{1+tg9}=\\ = (1+tg8)*\frac{2}{1+tg8} *(1+tg9)*\frac{2}{1+tg9}=2*2=4$
Ответ: 4.