已知x,y,z属于(0,派/2),sin^2x+sin^2y+sin^2z=1,求(sinx+siny+sinz)/(c

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/10 13:14:10

已知x,y,z属于(0,派/2),sin^2x+sin^2y+sin^2z=1,求(sinx+siny+sinz)/(cosx+cosy+cosz)的最大值

x,y,z属于(0,派/2)
sinx,cosx∈（0,1）
对于a>0,b>0,有不等式：开根号下（a^2+b^2)≥根号2*(a+b)/2
sin^2x+sin^2y+sin^2z=1
cosx=开根号下(sin^2y+sin^2z)≥根号2*(siny+sinz)/2
cosy=开根号下(sin^2x+sin^2z)≥根号2*(sinx+sinz)/2
cosz=开根号下(sin^2x+sin^2y)≥根号2*(sinx+siny)/2
仅当sinx=siny=sinz的时候,三式的等号成立.
三式相加得,cosx+cosy+cosz≥根号2*（sinx+siny+sinz)
所以(sinx+siny+sinz)/(cosx+cosy+cosz)≤根号2/2
仅当sinx=siny=sinz=根号3/3时,(sinx+siny+sinz)/(cosx+cosy+cosz)取最大值根号2/2

已知x,y,z属于(0,派/2),sin^2x+sin^2y+sin^2z=1,求(sinx+siny+sinz)/(c 证明sinx+siny+sinz-sin(x+y+z)=4sin((x+y)/2)sin((x+y)/2)sin((x+ 三角不等式证明证明sin(x+y)+sin(y+z)+sin(z+x)>sinx+siny+sinz+sin(x+y+z 已知sin(2x-y)5/13,siny=-3/5,x属于（派/2,派),y属于(-派/2,0),求sinx的值求函数z=sinx+siny+sin(x+y)(0 将sinx+siny+sinz-sin(x+y+z)化为积的形式已知x-y=派/3,且sin x-siny=1/2,求cos(x+y). 三角函数最值问题已知x,y,z为实数,求：f(x,y,z)=[sin(x-y)]^2+[sin(y-z)]^2+[sin 将sinx＋siny＋sinz－sin（x＋y＋z）化为积的形式已知sinx-siny=1/2,cosx-cosy=1/2,x、y均为锐角,求sin(x-y) 证明sin(x+y)sin(x-y)=（sinx）^2-(siny）^2. 已知x,y,z都是锐角,sin^2x+sin^2y+sin^2z=1,求tanx*tany*tanz的最值