向量a=(sina-cosa,2007),向量b=(sina+cosa,1)且向量a平行于向量b tan2a-1/cos2a=?

题目

向量a=(sina-cosa,2007),向量b=(sina+cosa,1)且向量a平行于向量b tan2a-1/cos2a=?

答案

∵向量a∥向量b,∴﹙sina-cosa﹚×1=﹙sina+cosa﹚×2007,∴tana=-1004／1003
tan2a-1/cos2a
=2tana／﹙1-tan²a﹚-﹙1+tan²a﹚／﹙1-tan²a﹚
=﹙tana-1﹚／﹙tana+1﹚
=2007