π/3
Пошаговое объяснение:
2cos7xcos2x=0,5(cos(7x+2x)+cos(7x-2x))=0,5(cos9x+cos5x)
cos(π+5x)=-cos5x
2cos7xcos2x+cos(π+5x)=-√2/2
2·0,5(cos9x+cos5x)+(-cos5x)=-√2/2
cos9x+cos5x-cos5x=-√2/2
cos9x=-√2/2
9x=±arccos(-√2/2)+2kπ=±(π-arccos(√2/2))+2kπ=±(π-π/4)+2kπ=±3π/4+2kπ
x=(±3π+8kπ)/9, k∈Z
min(x>0)=π/3
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π/3
Пошаговое объяснение:
2cos7xcos2x=0,5(cos(7x+2x)+cos(7x-2x))=0,5(cos9x+cos5x)
cos(π+5x)=-cos5x
2cos7xcos2x+cos(π+5x)=-√2/2
2·0,5(cos9x+cos5x)+(-cos5x)=-√2/2
cos9x+cos5x-cos5x=-√2/2
cos9x=-√2/2
9x=±arccos(-√2/2)+2kπ=±(π-arccos(√2/2))+2kπ=±(π-π/4)+2kπ=±3π/4+2kπ
x=(±3π+8kπ)/9, k∈Z
min(x>0)=π/3
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