(a^2+b^2)sin(A-B)=(a^2-b^2)sinC
∵sinC = sin{180°-（A+B)} = sin(A+B)
∴(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B)
a^2sin(A-B) + b^2sin(A-B) = a^2sin(A+B) - b^2sin(A+B)
a^2 { sin(A+B)-sin(A-B) } = b^2 { sin(A+B) + sin(A-B) }
a^2 * 2 cos { [(A+B)+(A-B)]/2 } sin { [(A+B)-(A-B)]/2 } = b^2 * 2 sin{ [(A+B)+(A-B)]/2 } cos { [(A+B)-(A-B)]/2 }
a^2 * 2 cosA sinB = b^2 * 2 sinA cosB
a^2/b^2 = sinA cosB/(cosA sinB)
(sinA/sinB)^2 = sinA cosB/(cosA sinB)
∵sinA≠0,sinB≠0,∴两边同乘以sinB/sinA
sinA/sinB = cosB/cosA
sinAcosA=sinBcosB
1/2sin(2A)=1/2(sin2B)
sin2A=sin2B
0＜2A,2B＜180°
∴2A=2B,或者2A+2B=180°
∴A=B,或A+B=90°
等腰三角形,或直角三角形