若tan(2x+y)=3,tanx=5,则tan(x+y)等于多少

题目

若tan(2x+y)=3,tanx=5,则tan(x+y)等于多少

答案

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