设cosx+cosy=t,由cosx+cosy=t,sinx+siny=√3/2,两个等式两边平方,得
cos²x+cos²y+2cosx·cosy=t²,sin²x+sin²y+2sinx·siny=3/4,两式相加,得
2+2(cosx·cosy+sinx·siny)=t²+3/4,所以有cos(x-y)=(t²-5/4)/2
由于-1≤cos(x-y)≤1,-1≤(t²-5/4)/2≤1,解不等式即可.