(a+b+c)/(sinA+sinB+sinC)=2R怎么证明?

分类: 作业答案 • 2021-12-18 16:11:17

问题描述：

(a+b+c)/(sinA+sinB+sinC)=2R
怎么证明?

答

正弦定理:a/sinA=b/sinB=c/sinC=2R
(a+b+c)/(sinA+sinB+sinC)=(2R sinA+2R sinB+2RsinC)/(sinA+sinB+sinC)
=2R (sinA+sinB+sinC)/(sinA+sinB+sinC)
=2R