[TEX]sinAsinB=3sin^2\frac{C}{2}(*)[/TEX]
[TEX]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}=2R\to sinA=a/2R ; sinB=b/2R ; sinC=c/2R[/TEX]
[TEX]sinAsinB=\frac{ab}{4R^2} ; sin(C/2)=\frac{c}{4Rcos(C/2)}[/TEX]
[TEX]3sin^2\frac{C}{2}=\frac{3c^2}{16R^2cos^2(C/2)}=\frac{3c^2}{8R^2(cosC+1)}[/TEX]
[TEX] cosC=\frac{a^2+b^2-c^2}{2ab} . (*)\to ab=\frac{3abc^2}{a^2+b^2-c^2+2ab}[/TEX]
[TEX]\to a^2+b^2+2ab=4c^2\to a+b=2c\to a,c,b [/TEX]là csc theo thứ tự đó