因α+β属于(3π/2,2π)
则cos(α+β)=根号(1-sin(α+β)*sin(α+β))=4/5
又α-β属于(π/2,π)
则sin(α-β)=根号(1-cos(α-β)*cos(α-β))=3/5
所以cos2α=cos[(α+β)+(α-β)]=cos(α+β)cos(α-β)-sin(α+β)sin(α-β)
=(4/5)*(-4/5)-(-3/5)(3/5)
=-16/25+9/25
=-7/25