• Предмет: Алгебра
  • Автор: Nurzhan94
  • Вопрос задан 8 лет назад

Помогите решить ................

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Ответы

Ответ дал: 7x8
0

1)

sin(alpha+beta)=sinalpha cosbeta+cosalpha sin beta

sin(alpha-beta)=sinalpha cosbeta-cosalpha sin beta

+___________

sin(alpha+beta)+sin(alpha-beta)=2sinalpha cosbeta

=========================================

cosfrac{2pi}{7}+cosfrac{4pi}{7}+cosfrac{6pi}{7}=

frac{2sinfrac{pi}{7} left(cosfrac{2pi}{7}+cosfrac{4pi}{7}+cosfrac{6pi}{7} right) }{2sinfrac{pi}{7}}=

frac{2sinfrac{pi}{7} cosfrac{2pi}{7}+2sinfrac{pi}{7}cosfrac{4pi}{7}+2sinfrac{pi}{7}cosfrac{6pi}{7}}{2sinfrac{pi}{7}}=

frac{sin left(frac{pi}{7} +frac{2pi}{7}right)+sinleft(frac{pi}{7} -frac{2pi}{7}right) +sin left(frac{pi}{7}+frac{4pi}{7} right)+sin left(frac{pi}{7}-frac{4pi}{7} right)+sin left(frac{pi}{7}+frac{6pi}{7} right)+sin left(frac{pi}{7}-frac{6pi}{7} right) }{2sinfrac{pi}{7}}=

frac{sinfrac{3pi}{7}+sinleft(-frac{pi}{7}right) +sin frac{5pi}{7} +sin left(-frac{3pi}{7} right)+sin pi+sin left(-frac{5pi}{7} right) }{2sinfrac{pi}{7}}=

frac{sinfrac{3pi}{7}-sinfrac{pi}{7}+sinfrac{5pi}{7} -sin frac{3pi}{7} +sin pi-sinfrac{5pi}{7} }{2sinfrac{pi}{7}}=

frac{-sinfrac{pi}{7} +sin pi }{2sinfrac{pi}{7}}=frac{-sinfrac{pi}{7} +0}{2sinfrac{pi}{7}}=frac{-sinfrac{pi}{7} }{2sinfrac{pi}{7}}=-frac{1}{2}

2)

cos(alpha+beta)=cosalpha cosbeta+sinalpha sin beta

cosn(alpha-beta)=cosalpha cosbeta-sinalpha sin beta

+___________

cos(alpha+beta)+cos(alpha-beta)=2cosalpha cosbeta

=========================================

cosfrac{2pi}{7}cosfrac{4pi}{7}+cosfrac{2pi}{7}cosfrac{6pi}{7}+cosfrac{4pi}{7}cosfrac{6pi}{7}=

frac{2cosfrac{2pi}{7}cosfrac{4pi}{7}}{2}+frac{2cosfrac{2pi}{7}cosfrac{6pi}{7}}{2}+frac{2cosfrac{4pi}{7}cosfrac{6pi}{7}}{2}=

frac{cos left(frac{2pi}{7} +frac{4pi}{7} right) +cosleft(frac{2pi}{7}-frac{4pi}{7} right)}{2}+frac{cos left(frac{2pi}{7} +frac{6pi}{7} right) +cosleft(frac{2pi}{7}-frac{6pi}{7} right)}{2}+frac{cos left(frac{4pi}{7} +frac{6pi}{7} right) +cosleft(frac{4pi}{7}-frac{6pi}{7} right)}{2}=

frac{cos frac{6pi}{7} +cosleft(-frac{2pi}{7} right)}{2}+frac{cos frac{8pi}{7} +cosleft(-frac{4pi}{7} right)}{2}+frac{cos frac{10pi}{7} +cosleft(-frac{2pi}{7} right)}{2}=

frac{cos frac{6pi}{7} +cosfrac{2pi}{7}}{2}+frac{cos frac{8pi}{7} +cosfrac{4pi}{7} }{2}+frac{cos frac{10pi}{7} +cosfrac{2pi}{7}}{2}=

frac{cosfrac{2pi}{7}+cosfrac{4pi}{7}+cos frac{6pi}{7} +cosfrac{2pi}{7}+cos frac{8pi}{7} +cos frac{10pi}{7} }{2}=

frac{cosfrac{2pi}{7}+cosfrac{4pi}{7}+cos frac{6pi}{7} +cosfrac{2pi}{7}+cos left(pi+frac{pi}{7} right) +cos left( pi+frac{3pi}{7}right) }{2}=

frac{cosfrac{2pi}{7}+cosfrac{4pi}{7}+cos frac{6pi}{7} +cosfrac{2pi}{7}-cos frac{pi}{7} -cos frac{3pi}{7} }{2}=

frac{-frac{1}{2} +cosfrac{2pi}{7}-cos frac{pi}{7} -cos frac{3pi}{7} }{2}=(*)

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sin(alpha+beta)=sinalpha cosbeta+cosalpha sin beta

sin(alpha-beta)=sinalpha cosbeta-cosalpha sin beta

+___________

sin(alpha+beta)+sin(alpha-beta)=2sinalpha cosbeta

cosfrac{2pi}{7}-cos frac{pi}{7} -cos frac{3pi}{7}=

frac{2sinfrac{pi}{7} left( cosfrac{2pi}{7}-cos frac{pi}{7} -cos frac{3pi}{7} right) }{2sinfrac{pi}{7}}=frac{2sinfrac{pi}{7} cosfrac{2pi}{7}-2sinfrac{pi}{7}cos frac{pi}{7} -2sinfrac{pi}{7}cos frac{3pi}{7} }{2sinfrac{pi}{7}}=

frac{sin left(frac{pi}{7} +frac{2pi}{7} right)+sinleft(frac{pi}{7} -frac{2pi}{7} right) -sin left(frac{pi}{7}+frac{pi}{7} right)-sinleft(frac{pi}{7}-frac{pi}{7} right) -sin left(frac{pi}{7}+ frac{3pi}{7} right) -sinleft(frac{pi}{7}- frac{3pi}{7} right) }{2sinfrac{pi}{7}}=

frac{sinfrac{3pi}{7} +sinleft(-frac{pi}{7} right) -sin frac{2pi}{7} -sin 0 -sin frac{4pi}{7} -sinleft(- frac{2pi}{7} right) }{2sinfrac{pi}{7}}=

frac{sinfrac{3pi}{7} -sinfrac{pi}{7} -sin frac{2pi}{7} -0 -sin frac{4pi}{7} +sin frac{2pi}{7} }{2sinfrac{pi}{7}}=

frac{sinfrac{3pi}{7} -sin frac{pi}{7} -sin frac{4pi}{7} }{2sinfrac{pi}{7}}=frac{sinfrac{3pi}{7} -sin frac{4pi}{7} -sin frac{pi}{7} }{2sinfrac{pi}{7}}=

frac{2cosfrac{frac{3pi}{7}+frac{4pi}{7} }{2}sinfrac{frac{3pi}{7}-frac{4pi}{7} }{2} -sin frac{pi}{7} }{2sinfrac{pi}{7}}=

frac{2cosfrac{pi}{2}sin left(frac{pi}{14}right) -sin frac{pi}{7} }{2sinfrac{pi}{7}}=

frac{0 -sin frac{pi}{7} }{2sinfrac{pi}{7}}=frac{ -sin frac{pi}{7} }{2sinfrac{pi}{7}}=-frac{1}{2}

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(*)=frac{-frac{1}{2} -frac{1}{2} }{2}=-frac{1}{2}

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