已知向量a=(cosα,sinα),b=(2,3),若a∥b
则
cosα/2=sinα/3
tanα=sinα/cosα=3/2
所以
sin^2α-sin2α
=(sin^2α-2sinαcosα)/(sin^2α+cos^2α) 分子分母同除以cos^2α,得
=(tan^2α-2tanα)/(tan^2α+1)
=(9/4 -2×3/2)/(9/4+1)
=(9-12)/(9+4)
=-3/13
已知向量a=(cosα,sinα),b=(2,3),若a∥b
则
cosα/2=sinα/3
tanα=sinα/cosα=3/2
所以
sin^2α-sin2α
=(sin^2α-2sinαcosα)/(sin^2α+cos^2α) 分子分母同除以cos^2α,得
=(tan^2α-2tanα)/(tan^2α+1)
=(9/4 -2×3/2)/(9/4+1)
=(9-12)/(9+4)
=-3/13