若tan(2x+y)=3,tanx=5,则tan(x+y)等于多少

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若tan(2x+y)=3,tanx=5,则tan(x+y)等于多少

若tan(2x+y)=3,tanx=5,则tan(x+y)等于多少
若tan(2x+y)=3,tanx=5,则tan(x+y)等于多少

若tan(2x+y)=3,tanx=5,则tan(x+y)等于多少
tan(2x+y)=tan[(x+y)+x]
tan(2x+y)=[tan(x+y)+tanx]/[1-tan(x+y)tanx]
3=[tan(x+y)+5]/[1-5tan(x+y)]
3-15tan(x+y)=tan(x+y)+5
16tan(x+y)=-2
tan(x+y)=-1/8

tan(2x)=2*tan(x)/(1-tanx*tanx)=-5/12
tan(2x+y)=3
=(tan(2x)+tany)/(1-tan2x*tany)=3
tany=-41/3
tan(x+y)=(tanx+tany)/(1-tanx*tany)=-1/8

设所求为n
tan(2x+y)=【n+tanx】/【1-ntanx】
n=-1/8

tan(2x+y)=[tanx+tan(x+y)]/[1-tanx*tan(x+y)]=3
[5+tan(x+y)]/[1-5*tan(x+y)]=3
[5+tan(x+y)]=3-15*tan(x+y)
tan(x+y)=-1/8

*为乘号