若向量a=(cosθ,-2sinθ),b=(sinθ,-3cosθ)若a·b=7/8,那么tanθ+1/tanθ的值为?

题目

若向量a=(cosθ,-2sinθ),b=(sinθ,-3cosθ)若a·b=7/8,那么tanθ+1/tanθ的值为?

答案

(cosθ,-2sinθ).(sinθ,-3cosθ)=7/8
cosθ.sinθ+6sinθcosθ=7/8
sinθcosθ =1/8
tanθ + 1/tanθ
= [(tanθ)^2+1]/tanθ
= 1/[ tanθ .(cosθ)^2]
=1/(sinθcosθ)
=8