Question

化简:cos(α-β)•cosβ-sin(α-β)sinβ 答案是cosα 要详细过程 加解说 急求 谢谢了！！

Answer 1

cos(α-β)=cosαcosβ+sinαsinβ

sin(α-β)=sinαcosβ-cosαsinβ

cos(α-β)•cosβ
=(cosαcosβ+sinαsinβ)*cosβ

=cosα(cosβ)^2+sinαsinβ*cosβ
sin(α-β)sinβ

=(sinαcosβ-cosαsinβ)*sinβ
=sinαcosβ*sinβ-cosα(sinβ)^2

cos(α-β)•cosβ-sin(α-β)sinβ

=[cosα(cosβ)^2+sinαsinβ*cosβ]-[sinαcosβ*sinβ-cosα(sinβ)^2]
=cosα(cosβ)^2+cosα(sinβ)^2+sinαsinβ*cosβ-sinαcosβ*sinβ
=cosα[(cosβ)^2+(sinβ)^2]
=cosα