作业帮cos2π/7cos4π/7cos8π/7要过程
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cos2π/7cos4π/7cos8π/7要过程
cos2π/7cos4π/7cos8π/7要过程
cos2π/7cos4π/7cos8π/7要过程
8sin2π/7cos2π/7cos4π/7cos8π/7/(8sin2π/7)
=4sin4π/7cos4π/7cos8π/7/(8sin2π/7)
=2sin8π/7cos8π/7/(8sin2π/7)
=sin16π/7/(8sin2π/7)
=sin2π/7/(8sin2π/7)
=1/8
cos(2π/7)cos(4π/7)cos(8π/7)
=2sin(2π/7)cos(2π/7)cos(4π/7)cos(8π/7)/【2sin(2π/7)】
=sin(4π/7)cos(4π/7)cos(8π/7)/【2sin(2π/7)】
=2sin(4π/7)cos(4π/7)cos(8π/7)/【4sin(2π/7)】
=sin(8π/7)cos(8π/7)...
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cos(2π/7)cos(4π/7)cos(8π/7)
=2sin(2π/7)cos(2π/7)cos(4π/7)cos(8π/7)/【2sin(2π/7)】
=sin(4π/7)cos(4π/7)cos(8π/7)/【2sin(2π/7)】
=2sin(4π/7)cos(4π/7)cos(8π/7)/【4sin(2π/7)】
=sin(8π/7)cos(8π/7)/【4sin(2π/7)】
=2sin(8π/7)cos(8π/7)/【8sin(2π/7)】
=sin(16π/7)/【8sin(2π/7)】
=sin(2π/7)/【8sin(2π/7)】
=1/8
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应该是cos(2π/7)cos(4π/7)cos(8π/7)吧？
如果是的话：
设A=cos(2π/7)cos(4π/7)cos(8π/7)
2Asin(2π/7)=2sin(2π/7)cos(2π/7)cos(4π/7)cos(8π/7)
2Asin(2π/7)=sin(4π/7)cos(4π/7)cos(8π/7)
4Asin(2π/7)=2sin(4π...
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应该是cos(2π/7)cos(4π/7)cos(8π/7)吧？
如果是的话：
设A=cos(2π/7)cos(4π/7)cos(8π/7)
2Asin(2π/7)=2sin(2π/7)cos(2π/7)cos(4π/7)cos(8π/7)
2Asin(2π/7)=sin(4π/7)cos(4π/7)cos(8π/7)
4Asin(2π/7)=2sin(4π/7)cos(4π/7)cos(8π/7)
4Asin(2π/7)=sin(8π/7)cos(8π/7)
8Asin(2π/7)=2sin(8π/7)cos(8π/7)
8Asin(2π/7)=sin(16π/7)
8Asin(2π/7)=sin[(14+2)π/7]
8Asin(2π/7)=sin(2π+2π/7)
8Asin(2π/7)=sin(2π/7)
8A=1
A=1/8
即：cos(2π/7)cos(4π/7)cos(8π/7)=1/8
收起