证明在△ABC中,(a-ccosB)/(b-ccosA)=sinB/sinA

来源:学生作业学帮网 编辑:学帮网 时间:2024/05/31 14:18:41

证明在△ABC中,(a-ccosB)/(b-ccosA)=sinB/sinA

由正弦定理
(a-ccosB)/(b-ccosA)
=(sinA-sinCcosB)/(sinB-sinCcosA)
=[sin(π-B-C)-sinCcosB]/[sin(π-A-C)-sinCcosA]
=[sin(B+C)-sinCcosB]/[sin(A+C)-sinCcosA]
=(sinBcosC+sinCcosB-sinCcosB)/(sinAcosC+sinCcosA-sinCcosA)
=(sinBcosC)/(sinAcosC)
=sinB/sinA