△ABC中∵sin(B+A)=2sin(B+C)∴sinC=2sinA为什么?

问题描述:

△ABC中∵sin(B+A)=2sin(B+C)∴sinC=2sinA为什么?

∵B+A+C=π
sin(B+A)=2sin(B+C)
∴sin(B+A)=sin(π-C)=sinC
2sin(B+C)=2sin(π-A)=2sinA
∴sinC=2sinA