令k=a/sinA=b/sinB=c/sinCa=ksinAb=ksinBc=ksinCcosA/a=cosB/b=cosC/ccosA/ksinA=cosB/ksinB=cosC/ksinCcosA/sinA=cosB/sinB=cosC/sinCcotA=cotB=cotC因为ABC都在0到180之间所以A=B=C等边三角形