解：1/3=sin[(x+y)-y]-sin[(x+y)-x] ```````=sin(x+y)cosy-cos(x+y)siny-sin(x+y)cosx+cos(x+y)sinx ```````=sin(x+y)(cosy-cosx)+cos(x+y)(sinx-siny) ```````=-sin(x+y)/2+cos(x+y)/3 1/3=-sin(x+y)/2+cos(x+y)/3……(1) 同理1/2=cos[(x+y)-y]-cos[(x+y)-x] ```````=cos(x+y)cosy+sin(x+y)siny-cos(x+y)cosx-sin(x+y)sinx ```````=sin(x+y)(siny-sinx)+cos(x+y)(cosy-cosx) ```````=-sin(x+y)/3-cos(x+y)/2 1/2=-sin(x+y)/3-cos(x+y)/2……(2) 联立(1)、(2)解得sin(x+y)=-12/13。
问：高一数学已知sinα=3/5,cosβ=12/13,且0<β<α<π,求cos(α-β)的值
答：解： cosα=±4/5,sinβ=5/13 cos(α-β)=cosαcosβ+sinαsinβ=63/65,-33/65详情>>
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