作CD垂直AB于D
a^2sin2B+b^2sin2A
=2a^2sinBcosB+2b^2sinAcosA
=2BD*CD+2AD*CD
=2AB*CD
=2absinC
sinAcosB+cosAsinB=sin(A+B)=sinC
2*(sinA/sinB)(sinBcosB)+2*(sinB/sinA)(sinAcosA) = 2*sinC
由正弦定理得：sinA/sinB=a/b 带入
(a/b)sin2A + (b/a)sin2B = 2*sinC
a^2sin2B+b^2sin2A = 2absinC
好难？？？？？
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