c2=a2+b2-2abcosC
2√3absinC=a2+b2+c2
则,2√3absinC+2abcosC=2(a2+b2)
即√3absinC+abcosC=a2+b2
得2sinC+30)=a2+b2
所以(a-b)^2=2ab[sin(C+30)-1]
因为(a-b)^2>=0,sin(C+30)-1