Докажите тождество:
[tex]4 \cos(x) \times \cos(60 - x) \times\cos(60 + x) [/tex]
60 - это градусы
[tex]4 \cos(x) \times \cos(60 - x) \times\cos(60 + x) [/tex]
60 - это градусы
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Ответ:
Объяснение:
Применяем формулу cosacosb=(1/2)[cos(a-b)+cos(a+b)]
4cosxcos(60°-x)cos(60°-x)=
=4cosx(1/2)[cos(60°-x-60°-x)+cos(60°-x+60°+x)=
=2cosx(cos2x+cos120°)=2cosx(cos2x-(1/2))=
=2cosxcos2x-cosx=
=2(1/2)[cos(x-2x)+cos(x+2x)]cosx
=2(1/2)[cosx+cos3x]-cosx=
cosx+cos3x-cosx=cos3x