已知A(2,3),B(1,4)且1/2向量AB=(sinα,cosβ),α,β∈(-π/2,π/2),且α+β=______

题目

已知A(2,3),B(1,4)且1/2向量AB=(sinα,cosβ),α,β∈(-π/2,π/2),且α+β=______

答案

1/2*AB=1/2*(1-2,4-3)=(-1/2,1/2)
sinα=-1/2
α=-π/6
cosβ=1/2
β=-π/3或π/3
α+β=-π/6+π/3=π/6
或
α+β=-π/6-π/3=-π/2