已知向量m=(cosα-√2/3,-1),n=(sinα,1),m与n为共线向量,且α∈(-π/2,0)求sin2α/(sinα-cosα

题目

已知向量m=(cosα-√2/3,-1),n=(sinα,1),m与n为共线向量,且α∈(-π/2,0)求sin2α/(sinα-cosα
已知向量m=(cosα-√2/3,-1),n=(sinα,1),m与n为共线向量,且α∈(-π/2,0)求sin2α/(sinα-cosα)的值.

答案

m与n为共线向量=>(cosα-√2/3)/(-1)=sinα/1-cosα+√2/3 = sinα√2/3 = (sinα+cosα)2/9 = 1+ sin2αsin2α = -7/9tan2α = -7/(4√2)-cosα+√2/3 = sinα√2/3 = (sinα+cosα) .(sinα-cosα)/(sinα-cosα)=...