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cos1/9π*cos2/9π*cos3/9π*cos4/9π=?怎么算?答案是1/16,

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/07 01:43:16
cos1/9π*cos2/9π*cos3/9π*cos4/9π=?怎么算?答案是1/16,
上下乘16sinπ/9sin2π/9sin3π/9sin4π/9
原式=(2sinπ/9cosπ/9)(2sin2π/9cos2π/9)(2sin3π/9cos3π/9)(2sin4π/9cos4π/9)/(1616sinπ/9sin2π/9sin3π/9sin4π/9)
=sin2π/9sin4π/9sin6π/9sin8π/9/(1616sinπ/9sin2π/9sin3π/9sin4π/9)
=sin2π/9sin4π/9sin(π-3π/9)sin(π-π/9)/(1616sinπ/9sin2π/9sin3π/9sin4π/9)
=sin2π/9sin4π/9sin3π/9sinπ/9/(1616sinπ/9sin2π/9sin3π/9sin4π/9)
=1/16