化简sin(2α+β)-2sinαcos(α+β)=?

网友回答

sin(2α+β)-2sinαcos(α+β)
=sin2αcosβ+sinβ2cos2α-2sinα(cosαcosβ-sinαsinβ)
=sin2αcosβ+sinβ2cos2α-2sinαcosαcosβ+2sinαsinαsinβ
=sin2αcosβ+sinβ2cos2α-sin2αcosβ+2sinαsinαsinβ
=sinβcos2α+2sinαsinαsinβ
=sinβ(cos2α+2sin^2α)
=sinβ(1-2sin^2α-2sin^2α)
=sinβ