已知向量a=(sinθ2,cosθ),b=(1,-cos θ ),0＜ θ＜派/2.若a·b=0,求tan θ 值

题目

已知向量a=(sinθ2,cosθ),b=(1,-cos θ ),0＜ θ＜派/2.若a·b=0,求tan θ 值

答案

∵a·b=0 ∴sin^2θ.1+cosθ.-cos θ=0 整理得sin^2θ=cos^2 θ
又∵0＜ θ＜π/2 ∴θ=π/4 故tan θ =1