Задание:
Найдите значение произвидения cos П/9 cos 2П/9 cos П/3 cos 4П/9 Помогите плиизз!)
Решение:
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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