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COS(π/9)COS(2π/9)COS(3π/9)COS(4π/9)=
题目详情
COS(π/9)COS(2π/9)COS(3π/9)COS(4π/9)=
▼优质解答
答案和解析
[sin(π/9)*cos(π/9)cos(2π/9)cos(3π/9)cos(4π/9)]/sin(π/9)
=[1/2*sin(π/9)*cos(π/9)cos(2π/9)cos(4π/9)]/sin(π/9)
={1/2*[1/2*sin(2π/9)cos(2π/9)cos(4π/9)]}/sin(π/9)
={1/4*[1/2*sin(4π/9)cos(4π/9)]}/sin(π/9)
={1/8*[1/2*sin(8π/9)]}/sin(π/9)
=1/16*[sin(8π/9)/sin(π/9)]
=1/16*[sin(π/9)/sin(π/9)]
=1/16
=[1/2*sin(π/9)*cos(π/9)cos(2π/9)cos(4π/9)]/sin(π/9)
={1/2*[1/2*sin(2π/9)cos(2π/9)cos(4π/9)]}/sin(π/9)
={1/4*[1/2*sin(4π/9)cos(4π/9)]}/sin(π/9)
={1/8*[1/2*sin(8π/9)]}/sin(π/9)
=1/16*[sin(8π/9)/sin(π/9)]
=1/16*[sin(π/9)/sin(π/9)]
=1/16
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