Question

高一，数学若sin(α+β)cosβ-cos(α+β)sinβ=0，则

sin(阿尔法+2贝塔）+sin(阿尔法-2β）=？？

Answer 1

sin(α+β)cosβ-cos(α+β)sinβ
=sin(α+β-β)
=sinα=0

sin(α+2β）+sin(α-2β）
=sinαcos2β+cosαsin2β+sinαcos2β-cosαsin2β
=2sinαcos2β
=0

Answer 2

sin(α+β)cosβ-cos(α+β)sinβ=0=sin(α+β-β)=sinα

sin(α+2β）+sin(α-2β）=2sinαcos(2β)=0

Answer 3

sin(α+β)cosβ-cos(α+β)sinβ=sinα=0
sin(α+2β)+sin(α-2β)=2sinαcos2β=0