已知sinx*cosy=1/4,则siny*cosx的取值范围是

题目

已知sinx*cosy=1/4,则siny*cosx的取值范围是
答案是【-3/4,3/4】,

答案

sinxcosy+cosxsiny=sin(x+y)sinxcosy-cosxsiny=sin(x-y)-1≤sin(x+y)≤1 -1≤1/4+cosxsiny≤1-5/4≤cosxsiny≤3/4-1≤sin(x-y)≤1 -1≤1/4-cosxsiny≤1 -5/4≤-cosxsiny≤3/4-3/4≤cosxsiny≤5/4综合得-3/4≤cosxsin...