求值:sinA*sinB*sinC(其中A=∏/14,B=3∏/14,C=5∏/14)答案为1/8
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![求值:sinA*sinB*sinC(其中A=∏/14,B=3∏/14,C=5∏/14)答案为1/8](/uploads/image/z/5183247-39-7.jpg?t=%E6%B1%82%E5%80%BC%EF%BC%9AsinA%2AsinB%2AsinC%28%E5%85%B6%E4%B8%ADA%3D%E2%88%8F%2F14%2CB%3D3%E2%88%8F%2F14%2CC%3D5%E2%88%8F%2F14%29%E7%AD%94%E6%A1%88%E4%B8%BA1%2F8)
求值:sinA*sinB*sinC(其中A=∏/14,B=3∏/14,C=5∏/14)答案为1/8
求值:sinA*sinB*sinC(其中A=∏/14,B=3∏/14,C=5∏/14)
答案为1/8
求值:sinA*sinB*sinC(其中A=∏/14,B=3∏/14,C=5∏/14)答案为1/8
首先利用 sinA=cos(π/2 -A).cosA=-cos(π -A)
你的题目中
sinA*sinB*sinC=cos(3π/7)cos(2π/7)cos(π/7)
=-cos(4π/7)cos(2π/7)cos(π/7)
=-cos(4π/7)cos(2π/7)cos(π/7)*sin(π/7)/sin(π/7)
=-sin(8π/7)/8sin(π/7)
=1/8
sinA*sinB*sinC
=cos6π/14*cos4π/14*cos2π/14
=[(cos6π/14*cos4π/14*cos2π/14)*2sin2π/14]/2sin2π/14
=[cos6π/14*cos4π/14*cos2π/14*2sin2π/14]/2sin2π/14
=[(cos6π/14*cos4π/14*sin4π/14]/2sin2π/1...
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sinA*sinB*sinC
=cos6π/14*cos4π/14*cos2π/14
=[(cos6π/14*cos4π/14*cos2π/14)*2sin2π/14]/2sin2π/14
=[cos6π/14*cos4π/14*cos2π/14*2sin2π/14]/2sin2π/14
=[(cos6π/14*cos4π/14*sin4π/14]/2sin2π/14
=1/2*[cos6π/14*sin8π/14]/2sin2π/14
=1/2*[cos6π/14*sin(π-8π/14)]/2sin2π/14
=1/2*[cos6π/14*sin6π/14]/2sin2π/14
=1/4sin12π/14/2sin2π/14
=1/8sin(π-12π/14)/sin2π/14
=1/8sin2π/14/sin2π/14
=1/8
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