在△ABC中,已知sinA/sinC=sin(A-B)/sin(B-C),求证,a*2,b*2,c*2成等差数列

题目

在△ABC中,已知sinA/sinC=sin(A-B)/sin(B-C),求证,a*2,b*2,c*2成等差数列

答案

sinA/sinC=sin(A-B)/sin(B-C)sinA/sinC=(sinAcosB-cosAsinB)/(sinBcosC-cosBsinC)a/sinA=b/sinB=c/sinCcosA=(b²+c²-a²)/(2bc)cosB=(c²+a²-b²)/(2ac)cosC=(a²+b²-c²)/(...