作业帮如果cosx+cosy-cos(x+y)=1.5,x,y为锐角,求x和y.
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如果cosx+cosy-cos(x+y)=1.5,x,y为锐角,求x和y.
如果cosx+cosy-cos(x+y)=1.5,x,y为锐角,求x和y.
如果cosx+cosy-cos(x+y)=1.5,x,y为锐角,求x和y.
cosx+cosy-cos(x+y)=3/2
--->2[cos(x+y)/2]^2-2[cos(x+y)/2][cos(x-y)/2]+1/2=0
[-2cos(x-y)/2]^2-4>=0
--->[cos(x-y)/2]^2>=1
[cos(x-y)/2]^2=1
x、y(0,兀) --->(x-y)/2(-兀/2,兀/2).
x=y,
x=y=兀/3.
cosx+cosy-cos(x+y)=1.5
式中x,y轮换对称，所以X Y 相等。
X =Y代入
2cosX-cos(2X)=3/2
2cosX-(2(cosX)^2 -1)=3/2
2(cosX)^2 -2cosX +1/2 =0
(cosX -1/2)^2 =0
cosX=1/2
X =π/3
所以，X =Y =π/3
如果cosx+cosy-cos(x+y)=1.5,x,y为锐角,求x和y.
如果cosx+cosy-cos(x+y)=0,x,y为锐角,求x和y.
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