已知b＜a＜0＜c,求|a|-|b a| |c-b|-|a-c|的值。

已知A:B:C:D=1:2:4:8,且A+B+C+D=2π，求cosAcosBcosCcosD的值

已知A:B:C:D=1:2:4:8,且A+B+C+D=2π，求cosAcosBcosCcosD的值 解:A:B:C:D=1:2:4:8→B=2A,C=4A,D=8A A+B+C+D=(1+2+4+8)A=2π,→15A=2π,A=2π/15 ∴cosAcosBcosCcosD= cos2π/15cos4π/15cos8π/15cos16π/15= [2sin2π/15cos2π/15cos4π/15cos8π/15cos16π/15]/[2sin2π/15]= [sin4π/15ccos4π/15cos8π/15cos16π/15]/[2sin2π/15]= [2sin4π/15ccos4...全部

  已知A:B:C:D=1:2:4:8,且A+B+C+D=2π，求cosAcosBcosCcosD的值 解:A:B:C:D=1:2:4:8→B=2A,C=4A,D=8A A+B+C+D=(1+2+4+8)A=2π,→15A=2π,A=2π/15 ∴cosAcosBcosCcosD= cos2π/15cos4π/15cos8π/15cos16π/15= [2sin2π/15cos2π/15cos4π/15cos8π/15cos16π/15]/[2sin2π/15]= [sin4π/15ccos4π/15cos8π/15cos16π/15]/[2sin2π/15]= [2sin4π/15ccos4π/15cos8π/15cos16π/15]/[4sin2π/15]= [sin8π/15cos8π/15cos16π/15]/[4sin2π/15]= [2sin8π/15cos8π/15cos16π/15]/[8sin2π/15]= [sin16π/15cos16π/15]/[8sin2π/15]= [2sin16π/15cos16π/15]/[16sin2π/15]= [sin32π/15]/[16sin2π/15]= [sin(2π+2π/15)]/[16sin2π/15]= [sin(2π/15)]/[16sin2π/15]= 1/16 。
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