已知α.β为锐角,且3(sinα)^2+2(sinβ)^2=1,3sin2α-2sin2β=0求α+2β

已知α.β为锐角,且3(sinα)^2+2(sinβ)^2=1,3sin2α-2sin2β=0求α+2β
已知α.β为锐角,且3(sinα)^2+2(sinβ)^2=1,3sin2α-2sin2β=0求α+2β

已知α.β为锐角,且3(sinα)^2+2(sinβ)^2=1,3sin2α-2sin2β=0求α+2β
cos(α+2β)
=cosαcos2β-sinαsin2β
=cosα(1-2(sinβ)^2)-sinαsin2β
=cosα(3(sinα)^2)-sinα(3*sin(2α)/2)
=3sin(2α)sinα/2-3sin(2α)*sinα/2
=0
又α,β为锐角,所以0