2sin2CcosC-sin(2C+C)=根号3(1-cosC)
2sin2CcosC-(sin2CcosC+cos2CsinC)=根号3*（2sin^2C/2）
sin2CcosC-cos2CsinC=根号3*2sin^2C/2
sin(2C-C)=2根号3sin^2C/2
2sinC/2cosC/2=2根号3sin^2C/2
tanC/2=根号3/3
C/2=Pai/6
C=Pai/3
(2)sinC+sin(B-A)=2sin2A
sin(A+B)+sin(B-A)=2sin2A
2sinBcosA=2*2sinAcosA
sinB=2sinA
即有b=2a
c=AB=2,c^2=a^2+b^2-2abcosC
4=a^2+4a^2-2a*2a*1/2=3a^2
a^2=4/3
S=1/2absinC=1/2a*2a*根号3/2=4/3*根号3/2=2/3*根号3.