用正弦定理a/sinA=b/sinB=c/sinC=2R求解
∵a^2=b(b+c)
∴sin^2A=sin^2B+sinB*sinC
∴(sinA+sinB)(sinA-sinB)=sinB*sin(A+B)
∴2sin[(A+B)/2]cos[(A-B)/2]*2cos[(A+B)/2]sin[(A-B)/2]
=sinB*sin(A+B)
∴sin)(A+B)*sin(A-B)=sinB*sin(A+B)
∴sin(A-B)=sinB
∴A-B=B
∴A=2Bsin^2A=sin^2B+sinB*sinC
sin^2A-sin^2B=sinB*sinC
∴(sinA+sinB)(sinA-sinB)=sinB*sin(A+B)sin^2A-sin^2B平方差公式呀 =(sinA+sinB)(sinA-sinB)2倍角公式sinA+sinB=2sin[(A+B)/2]cos[(A-B)/2]*任意角公式?jīng)]有