△ABC中,若a(bcosB-ccosC)=(b^2-c^2)cosA,判断三角形的形状

把a,b,c分别换成sinA,sinB,sinC
sinA(sinBcosB-sinCcosC)=(sin^2B-sin^2C)cosA
sinA(sin2B-sin2C)=(cos2C-cos2B)cosA
sinAsin2B-sinAsin2C=cosAcos2C-cosAcos2B
sinAsin2B+cosAcos2B=cosAcos2C+sinAsin2C
cos(A-2B)=cos(A-2C)
A-2B=A-2C或A-2B=-(A-2C)
B=C或A=B+C
所以:等腰三角形或直角三角形.