已知cos(x)=1/7 cos(x+y)=-11/14 且x,y属于(0,90) 求cos(y)

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已知cos(x)=1/7 cos(x+y)=-11/14 且x,y属于(0,90) 求cos(y)
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已知cos(x)=1/7 cos(x+y)=-11/14 且x,y属于(0,90) 求cos(y)
已知cos(x)=1/7 cos(x+y)=-11/14 且x,y属于(0,90) 求cos(y)

已知cos(x)=1/7 cos(x+y)=-11/14 且x,y属于(0,90) 求cos(y)
因为sin^x+cos^x=1
x,y属于(0,90) ,所以sinx>0
sinx=4*根号3/7
cos^(x+y)+sin^(x+y)=1
sin(x+y)>0
所以sin(x+y)=5*根号3/14
因为cosy=cos(x+y-x)=cos(x+y)cosx+sin(x+y)sinx
=-(11/14)*(1/7)+(5*根号3/14)*(4*根号3/7)
=-11/98+60/98
=49/98
=1/2

由cos(x)可求得sin(x)的值
cos(x+y)=cos(x)*cos(y)-sin(x)*sin(y)
代入sin(x) cos(x)再用cos(y)表示sin(y)
便可求得cos(y)=71/98