数学2cosθcos2θ-cosθ=?

问题描述:

数学2cosθcos2θ-cosθ=?
2cosθcos2θ-cosθ=?据说答案好像是2cosθcos2θ-cosθ=cos3θ.

倒着推
cos3θ
=cos(θ+2θ)
=cosθcos2θ-sinθsin2θ
=cosθcos2θ-sinθ(2sinθcosθ)
=cosθcos2θ-(2sinθsinθ)cosθ
=cosθcos2θ-(1-cos2θ)cosθ
=cosθcos2θ-cosθ+cosθcos2θ
=2cosθcos2θ-cosθ