x,y,z屬于(0,派/2)
sinx,cosx∈（0,1）
對(duì)于a>0,b>0,有不等式：開根號(hào)下（a^2+b^2)≥根號(hào)2*(a+b)/2
sin^2x+sin^2y+sin^2z=1
cosx=開根號(hào)下(sin^2y+sin^2z)≥根號(hào)2*(siny+sinz)/2
cosy=開根號(hào)下(sin^2x+sin^2z)≥根號(hào)2*(sinx+sinz)/2
cosz=開根號(hào)下(sin^2x+sin^2y)≥根號(hào)2*(sinx+siny)/2
僅當(dāng)sinx=siny=sinz的時(shí)候,三式的等號(hào)成立.
三式相加得,cosx+cosy+cosz≥根號(hào)2*（sinx+siny+sinz)
所以(sinx+siny+sinz)/(cosx+cosy+cosz)≤根號(hào)2/2
僅當(dāng)sinx=siny=sinz=根號(hào)3/3時(shí),(sinx+siny+sinz)/(cosx+cosy+cosz)取最大值根號(hào)2/2