Question

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

Answer 1

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.