在△ABC中,已知(a+b)/a=sinB/(sinB-sinA),且cos(A-B)+cosC=1-cos2C,试确定△ABC的_数学解答

在△ABC中,已知(a+b)/a=sinB/(sinB-sinA),且cos(A-B)+cosC=1-cos2C,试确定△ABC的形状.

人气：423 ℃　时间：2019-08-20 14:48:20

解答

∵cosC=cos(-C)=-cos(180°-C)=-cos(A+B)cos2C=1-2sin^2(C)∴cos（A-B)+cosC=1-cos2C可转换为cos（A-B）-cos（A+B）=2sin^2C∵cos(A+B)=cosA·cosB-sinA·sinBcos(A-B)=cosA·cosB+sinA·sinβB所以cos（A-B）-cos（...