已知3sin^2 α+2sin^2 β=1,3sin2α-2sin2β=0 求证cos(α+2β)=0
问题描述:
已知3sin^2 α+2sin^2 β=1,3sin2α-2sin2β=0 求证cos(α+2β)=0
答
3sin^2 α+2sin^2 β=1①
3sin2α-2sin2β=0 ②
①==>3sin^2 α=1-2sin^2β=cos2β
②==>sin2β=3/2sin2α=3sinαcosα
∴cos(α+2β)
=cosαcos2β-sinαsin2β
=cosα*3sin^2α-sinα*3sinαcosα
=0