lg(sinA+sinC)=2lgsinB-lg(sinC-sinA)
lg(sinA+sinC)+lg(sinC-sinA)=2lgsinB
(sinA+sinC)(sinC-sinA)=sin²B
sin²C-sin²A=sin²B
根据正弦定理
a/sinA=b/sinB=c/sinC
a²+b²=c²
△ABC为rt△