1)cos(x+y)=-1,说明x+y=180度,
sin(x+y)=√[1-cos^2(x+y)]=0
若,X在第一象限时,
令,sinx=2/r,cosx=1/r,则
r=√5,
sinx=2/√5,cosx=1/√5.
siny=sin(x+y-x)=sin(x+y)*cosx-cos(x+y)*sinx
=0-(-1)*2/√5
=2√5/5.
cosy=cos(x+y-x)=cos(x+y)cosx+sin(x+y)sinx
=(-1)*1/√5+0
=-√5/5.
tany=siny/cosy=-2.
2)tanx=4√3,xy为锐角,
sinx=4√3/r,cosx=1/r,
r=7.
sinx=4√3/7,cosx=1/7.
cos(x+y)=-11/14,
sin(x+y)=√[1-(-11/14)^2]=5√3/14.
cosy=cos(x+y-x)=cos(x+y)cosx+sin(x+y)sinx
=1/2.
3)x+y=135度,
因为:tan(x+y)=tan135=-1=(tanx+tany)/(1-tanxtany)
所以,
-(tanx+tany)=1-tanxtany.
（1-tanx)(1-tany)=1-(tanx+tany)+tanxtany
=1+(1-tanxtany)+tanxtany
=2.