求2cos(9兀/13)cos(兀/13)+cos(5兀/13)+cos(3兀/13)的值急 !!!!
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![求2cos(9兀/13)cos(兀/13)+cos(5兀/13)+cos(3兀/13)的值急 !!!!](/uploads/image/z/14406431-23-1.jpg?t=%E6%B1%822cos%EF%BC%889%E5%85%80%2F13%EF%BC%89cos%EF%BC%88%E5%85%80%2F13%EF%BC%89%2Bcos%EF%BC%885%E5%85%80%2F13%EF%BC%89%2Bcos%EF%BC%883%E5%85%80%2F13%EF%BC%89%E7%9A%84%E5%80%BC%E6%80%A5+%EF%BC%81%EF%BC%81%EF%BC%81%EF%BC%81)
求2cos(9兀/13)cos(兀/13)+cos(5兀/13)+cos(3兀/13)的值急 !!!!
求2cos(9兀/13)cos(兀/13)+cos(5兀/13)+cos(3兀/13)的值
急 !!!!
求2cos(9兀/13)cos(兀/13)+cos(5兀/13)+cos(3兀/13)的值急 !!!!
2cos(9兀/13)cos(兀/13)+cos(5兀/13)+cos(3兀/13)
=cos(9兀/13+兀/13)+cos(9兀/13-兀/13)+cos(5兀/13)+cos(3兀/13)
=cos(10兀/13)+cos(8兀/13))+cos(5兀/13)+cos(3兀/13)
=-cos(3兀/13)-cos(5兀/13)+cos(5兀/13)+cos(3兀/13)
=0
用和差化积cos(5兀/13)+cos(3兀/13)=2cos4/13πcosπ/13
2cos(9兀/13)cos(兀/13)+2cos4/13πcosπ/13 cos9/13π+cos4/13π=cosπ
所以=2cos9兀/13)cos(兀/13)-2cos4/13πcosπ/13 =0