已知sinx+cosy=2/3，求cosx+siny的取值范围

cos(x-y)的范围,是余弦函数的值域,不管cos内有多少东东,它都是[-1,1]

其它的,既然你知道,我就不多写了.

还是写一下吧,
(sinx+siny)^2+(cosx+cosy)^2=4/9+(cosx+cosy)^2
=sinx2+siny2+cosx2+cosy2+2(sinxsiny+cosxcosy)
=2+2cos(x-y)
所以,(cosx+cosy)^2=14/9-cos(x-y)

因为-1<=cos(x-y)<=1
所以,-1<=-cos(x-y)<=1
5/9<=14/9-cos(x-y)<=23/9

所以,5/9<=(cosx+cosy)^2<=23/9

所以,-根号23/3<=cosx+cosy<=-根号5/3
或根号5/3<=cosx+cosy<=根号23/3