cosп/9*cos2п/9*соs4п/9 как решить помогите пж))). Created by ranaexotic. algebra-ru

9 как решить помогите пж)))...

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cosп/9*cos2п/9*соs4п/9 как решить помогите пж)))

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Andrusha228 Cos(n/9)cos(2n/9)cos(n/3)cos(4n/9)=(cos(n/9)cos(n/3))(cos(2n/9)cos(4n/9))=(cos(4n/9)+cos(2n/9))/2 * (cos(6n/9)+cos(2n/9))/2 = (cos(4n/9)cos(6n/9)+cos(2n/9)cos(6n/9)+cos(4n/9)cos(2n/9)+cos(2n/9)cos(2n/9))/4= ((cos(10n/9)+cos(2n/9))/2+(cos(8n/9)+cos(4n/9))/2+(cos(6n/9)+cos(2n/9))/2+(cos(4n/9)+1)/2)/4=(cos(10n/9)+cos(2n/9)+cos(8n/9)+cos(4n/9)+cos(6n/9)+cos(2n/9)+cos(4n/9)+1)/8= ((cos(10n/9)+cos(8n/9))+2(cos(2n/9)+cos(4n/9))+cos(6n/9)+1)/8= (2cos(18n/9)cos(2n/9)+4cos(6n/9)cos(2n/9)+cos(6n/9)+1)/8=(2cos(2n)cos(2n/9)+4cos(2n/3)cos(2n/9)+cos(2n/3)+1)/8=(-2cos(2n/9)+2cos(2n/9)+1/2+1)/8=(1/2+1)/8=(3/2)/8=3/16

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ranaexotic код ответа 1/8

Andrusha228 код? ну сократи потом

ranaexotic а да правильно так долго решается ужас

Andrusha228 ага

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