用正弦定理换掉,
sinAcosA+sinBcosB=SinCcos C
sin2A+sin2B=sin2C
和差化积,
2sin(A+B)cos(A-B)=2sinCcosC
即cos(A-B)=cosC=-cos(A+B)
所以展开,cosAcosB+sinAsinB=-cosAcosB+sinAsinB
于是cosAcosB=0,所以是直角三角形