若sinx+siny=根2/2 求cosx+cosy的取值范围

(sinx+siny)^2=sin^2x+sin^2y+2*sinx*siny=1/2
(cosx+cosy)^2
=cos^2x+cos^2y+2*cosx*cosy
=1-sin^x+1-sin^2y-2*sinx*siny+2*sinx*siny+2*cosx*cosy
=2-1/2+2*cos(x-y)
=3/2+2*cos(x-y)
0<=(cosx+cosy)^2<=7/2
0<=cosx+cosy<=根号14/2


good

@林汐196 这坟是你挖的吗？