热心网友
sinx+siny=2/3 ,求cosx+cosy 的范围设 cosx + cosy = k ,则 (cosx)^2 +(cosy)^2 +2cosxcosy=k^2因 sinx+siny=2/3 ，所以(sinx)^2 +(siny)^2 +2sinxsiny=4/9所以 2 + 2cos(x-y)=k^2 + 4/9 ,即 2cos(x-y) = k^2 -14/9所以 -14/9 ≤ k^2 -14/9 ≤2所以 -(4√2)/3 ≤k≤ (4√2)/3
sinx+siny=2/3 ,求cosx+cosy 的范围设 cosx + cosy = k ,则 (cosx)^2 +(cosy)^2 +2cosxcosy=k^2因 sinx+siny=2/3 ，所以(sinx)^2 +(siny)^2 +2sinxsiny=4/9所以 2 + 2cos(x-y)=k^2 + 4/9 ,即 2cos(x-y) = k^2 -14/9所以 -14/9 ≤ k^2 -14/9 ≤2所以 -(4√2)/3 ≤k≤ (4√2)/3