(cosA)^2-(cosB)^2
=(1+cos2A)/2-(1+cos2B)/2
=(cos2A-cos2B)/2
=sin(A+B)sin(B-A)=sinCsin(B-A)
(b-c)(cosA)^2=b(cosB)^2-c(cosC)^2,
--->b(cosA)^2-c(cosA)^2=b(cosC)^2-c(cosC)^2
--->b[(cosA)^2-(cosB)^2]-c[(cosA)^2-(cosC)^2]=0
--->bsinCsin(B-A)-csinBsin(C-A)=0
[b/sinB=c/sinC--->bsinC=csinB]
--->bsinC[sin(B-A)-sin(C-A)]=0 [bsinC0]
--->2cos[(B+C-2A)/2]sin[(B-C)/2]=0
--->cos(90°-3A/2)sin(B/2-C/2)=0
--->sin(3A/2)sin(B/2-C/2)=0
sin(3A/2)=0--->3A/2=180°--->A=120°或
sin(B/2-C/2)=0--->B=C.
--->△ABC是一个有一个角是120°的三角形,或者是等腰三角形.