lg(sinA+sinC)=2lgsinB-lg(sinC-sinA)
lg(sinA+sinC)=lg[sin²B/(sinC-sinA)]
(sinA+sinC)=sin²B/(sinC-sinA)
(sinC+sinA)(sinC-sinA)=sin²B
sin²C-sin²A=sin²B
由正弦定理得
c²-a²=b²
a²+b²=c²,三角形是直角三角形.
lg(sinA+sinC)=2lgsinB-lg(sinC-sinA)
lg(sinA+sinC)=lg[sin²B/(sinC-sinA)]
(sinA+sinC)=sin²B/(sinC-sinA)
(sinC+sinA)(sinC-sinA)=sin²B
sin²C-sin²A=sin²B
由正弦定理得
c²-a²=b²
a²+b²=c²,三角形是直角三角形.