已知cos(x+y)=1/3,cos(x-y)+2/3,且0

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cos(x+y)=1/3,cos(x-y)=2/3.
0＜x＜90º,60º＜y＜90º
∴可得:0＜x＜30＜60＜y＜90º
sin(x+y)=(2√2)/3.cos(x+y)=1/3.
sin(y-x)=(√5)/3,cos(y-x)=2/3.
[[[1]]]
cos2x=cos[(y+x)-(y-x)]
=cos(x+y)cos(y-x)+sin(x+y)sin(y-x)
=(2/9)+[(2√10)/9]
=2(1+√10)/9
[[[2]]]
1=cos(x+y)+cos(x-y)=2cosxcosy
1/3=cos(x-y)-cos(x+y)=-2sinxsin(-y)
∴sinxsiny=1/6
cosxcosy=1/2
∴两式相除,可得
tanxtany=1/3

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