Предмет: Алгебра,
автор: ghvbntq
(sin 11П/18 - sin П/18)/(cos 11П/18 - cos П/18)
Ответы
Автор ответа:
0
Формулы, которые нам понадобятся:
![boxed{diplaystyle sin alpha-sin beta=2sin frac{alpha-beta}{2} cdot cos frac{alpha+beta}{2}} boxed{diplaystyle sin alpha-sin beta=2sin frac{alpha-beta}{2} cdot cos frac{alpha+beta}{2}}](https://tex.z-dn.net/?f=boxed%7Bdiplaystyle+sin+alpha-sin+beta%3D2sin+frac%7Balpha-beta%7D%7B2%7D+cdot+cos+frac%7Balpha%2Bbeta%7D%7B2%7D%7D+)
![boxed{displaystyle cos alpha - cos beta =-2sin frac{alpha+beta}{2} cdot sin frac{alpha-beta}{2}} boxed{displaystyle cos alpha - cos beta =-2sin frac{alpha+beta}{2} cdot sin frac{alpha-beta}{2}}](https://tex.z-dn.net/?f=boxed%7Bdisplaystyle+cos+alpha+-+cos+beta+%3D-2sin+frac%7Balpha%2Bbeta%7D%7B2%7D+cdot+sin+frac%7Balpha-beta%7D%7B2%7D%7D)
![displaystyle frac{sin frac{11 pi}{18}-sin frac{pi}{18}}{cos frac{11 pi}{18}-cos frac{pi}{18}}=frac{2sin frac{frac{11 pi}{18}- frac{pi}{18}}{2} cdot cos frac{frac{11 pi}{18}+frac{pi}{18}}{2}}{-2sin frac{frac{11 pi}{18}+ frac{pi}{18}}{2} cdot sin frac{frac{11 pi}{18}- frac{pi}{18}}{2}}= displaystyle frac{sin frac{11 pi}{18}-sin frac{pi}{18}}{cos frac{11 pi}{18}-cos frac{pi}{18}}=frac{2sin frac{frac{11 pi}{18}- frac{pi}{18}}{2} cdot cos frac{frac{11 pi}{18}+frac{pi}{18}}{2}}{-2sin frac{frac{11 pi}{18}+ frac{pi}{18}}{2} cdot sin frac{frac{11 pi}{18}- frac{pi}{18}}{2}}=](https://tex.z-dn.net/?f=displaystyle+frac%7Bsin+frac%7B11+pi%7D%7B18%7D-sin+frac%7Bpi%7D%7B18%7D%7D%7Bcos+frac%7B11+pi%7D%7B18%7D-cos+frac%7Bpi%7D%7B18%7D%7D%3Dfrac%7B2sin+frac%7Bfrac%7B11+pi%7D%7B18%7D-+frac%7Bpi%7D%7B18%7D%7D%7B2%7D+cdot+cos+frac%7Bfrac%7B11+pi%7D%7B18%7D%2Bfrac%7Bpi%7D%7B18%7D%7D%7B2%7D%7D%7B-2sin+frac%7Bfrac%7B11+pi%7D%7B18%7D%2B+frac%7Bpi%7D%7B18%7D%7D%7B2%7D+cdot+sin+frac%7Bfrac%7B11+pi%7D%7B18%7D-+frac%7Bpi%7D%7B18%7D%7D%7B2%7D%7D%3D)
![displaystyle = frac{2sin (frac{10 pi}{18} cdot frac{1}{2}) cdot cos (frac{12 pi}{18} cdot frac{1}{2})}{-2sin( frac{12 pi}{18} cdot frac{1}{2}) cdot sin(frac{10 pi}{18}cdot frac{1}{2})}=frac{2sin frac{5 pi}{18}cdot cos frac{pi}{3}}{-2sin frac{pi}{3} cdot sin frac{5 pi}{18}}= displaystyle = frac{2sin (frac{10 pi}{18} cdot frac{1}{2}) cdot cos (frac{12 pi}{18} cdot frac{1}{2})}{-2sin( frac{12 pi}{18} cdot frac{1}{2}) cdot sin(frac{10 pi}{18}cdot frac{1}{2})}=frac{2sin frac{5 pi}{18}cdot cos frac{pi}{3}}{-2sin frac{pi}{3} cdot sin frac{5 pi}{18}}=](https://tex.z-dn.net/?f=displaystyle+%3D+frac%7B2sin+%28frac%7B10+pi%7D%7B18%7D+cdot+frac%7B1%7D%7B2%7D%29+cdot+cos+%28frac%7B12+pi%7D%7B18%7D+cdot+frac%7B1%7D%7B2%7D%29%7D%7B-2sin%28+frac%7B12+pi%7D%7B18%7D+cdot+frac%7B1%7D%7B2%7D%29+cdot+sin%28frac%7B10+pi%7D%7B18%7Dcdot+frac%7B1%7D%7B2%7D%29%7D%3Dfrac%7B2sin+frac%7B5+pi%7D%7B18%7Dcdot+cos+frac%7Bpi%7D%7B3%7D%7D%7B-2sin+frac%7Bpi%7D%7B3%7D+cdot+sin+frac%7B5+pi%7D%7B18%7D%7D%3D)
![displaystyle = frac{cos frac{pi}{3}}{-sin frac{pi}{3}}=-ctg frac{pi}{3}=boxed{- frac{sqrt 3}{3}} displaystyle = frac{cos frac{pi}{3}}{-sin frac{pi}{3}}=-ctg frac{pi}{3}=boxed{- frac{sqrt 3}{3}}](https://tex.z-dn.net/?f=displaystyle+%3D+frac%7Bcos+frac%7Bpi%7D%7B3%7D%7D%7B-sin+frac%7Bpi%7D%7B3%7D%7D%3D-ctg+frac%7Bpi%7D%7B3%7D%3Dboxed%7B-+frac%7Bsqrt+3%7D%7B3%7D%7D)
Похожие вопросы
Предмет: История,
автор: FRBK1
Предмет: Другие предметы,
автор: kazaninasvetlan
Предмет: Биология,
автор: muhamediyar
Предмет: История,
автор: LovLov
Предмет: Литература,
автор: Лидусик99