已知cos(α+β)cosα+sin(α+β)sinα=√6/3,则cos2β=多少

问题描述:

已知cos(α+β)cosα+sin(α+β)sinα=√6/3,则cos2β=多少

答:
cos(α+β)cosα+sin(α+β)sinα=√6/3
cos(α+β-a)=√6/3
cosβ=√6/3
cos2β
=2(cosβ)^2-1
=2*(√6/3)^2-1
=2*(6/9)-1
=1/3
所以:cos2β=1/3