Ответы
Ответ дал:
0
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}](https://tex.z-dn.net/?f=1%29+tg36%3D+tg%2845-9%29%3Dfrac%7Btg45-tg9%7D%7B1%2Btg45tg9%7D+%3D+frac%7B1-tg9%7D%7B1%2Btg9%7D+%5C%0A2%29+tg37%3D+tg%2845-8%29%3Dfrac%7Btg45-tg8%7D%7B1%2Btg45tg8%7D+%3D+frac%7B1-tg8%7D%7B1%2Btg8%7D+ "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](https://tex.z-dn.net/?f=%3D%281%2Btg8%29%281%2Bfrac%7B1-tg8%7D%7B1%2Btg8%7D+%29%281%2Btg9%29%281%2Bfrac%7B1-tg9%7D%7B1%2Btg9%7D+%29%3D%5C%0A%3D%281%2Btg8%29%2Afrac%7B1%2Btg8%2B1-tg8%7D%7B1%2Btg8%7D+%2A%281%2Btg9%29%2Afrac%7B1%2Btg9%2B1-tg9%7D%7B1%2Btg9%7D%3D%5C%0A%3D+%281%2Btg8%29%2Afrac%7B2%7D%7B1%2Btg8%7D+%2A%281%2Btg9%29%2Afrac%7B2%7D%7B1%2Btg9%7D%3D2%2A2%3D4 "=(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.
(1+tg8)(1+tg9)(1+tg36)(1+tg37) =
Ответ: 4.
Приложения:
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