已知a、b为锐角,且满足3sin^2a+2sin^2b=1,3sin2a-2sin2b.求证a+2b=3.14/2

由3sin2a-2sin2b.故6sina*cosa=4sinb*cosb,
故3sina*根号(1-(sina)^2)=2sinb*根号(1-(sinb)^2),
故3*根号((sina)^2-(sina)^4)=2*根号((sinb)^2-(sinb)^4)
故9(sina)^2-9(sina)^4=4(sinb)^2-4(sinb)^4=2*(1-3(sina)^2)-[1-(sina)^2]^2
=2-6(sina)^2-1+6(sina)^2-9(sina)^4
故9(sina)^2=1,sina=1/3,
故2(sinb)^2=1-3*1/9=2/3,(sinb)^2=1/3,cos2b=1-2(sinb)^2=1/3,
故sin(a+2b)=sina*cos2b+cosa*sin2b=1/3*1/3+2*根号2/3*2*根号2/3=1,
故a+2b=派/2=a+2b=3.14/2

3sin2a-2sin2b,少了点什么?