有两种方法: 1。cos(π/9)cos(2π/9)cos(4π/9) =[sin(π/9)cos(π/9)cos(2π/9)cos(4π/9)]/sin(π/9) =[(1/2)sin(2π/9)cos(2π/9)cos(4π/9)]/sin(π/9) =[1/4)sin(4π/9)cos(4π/9)]/sin(π/9) =[(1/8)sin(8π/9)]/sin(π/9) =(1/8)sin(π/9)/sin(π/9) =1/8 2。
对偶法 令A=cos(π/9)cos(2π/9)cos(4π/9) B=sin(π/9)sin(2π/9)sin(4π/9) A*B=cos(π/9)cos(2π/9)cos(4π/9)sin(π/9)sin(2π/9)sin(4π/9) =1/8sin(2π/9)sin(4π/9)sin(8π/9) =1/8sin(2π/9)sin(4π/9)sin(π/9) =1/8 *B 所以A=1/8 (这是种很好的方法,应用很广!) 。
设S=cos(π/9)cos(2π/9)cos(4π/9) S*sin(π/9)=sin(π/9)cos(π/9)cos(2π/9)cos(4π/9) =(1/2)sin(2π/9)cos(2π/9)cos(4π/9) =(1/4)sin(4π/9)cos(4π/9) =(1/8)sin(8π/9) =(1/8)sin(π/9) S=1/8 即cos(π/9)cos(2π/9)cos(4π/9)=1/8
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