If the Cosines of the angles of a triangle are proportional to opposite sides, then the triangle is

Given     CosAa=CosBb=cosCc; Also   a=2RsinA, b=2R​ sinB, c=2RsinC       by sine rule⇒CosA2RsinA=CosB2R​ sinB=cosC2RsinC⇒cotA=cotB=cotC⇒A=B=C⇒the  triangle is equilateral