已知tan(x+π4)=2,则tanx/tan2x的值为_.

问题描述:

已知tan(x+

π
4
)=2,则
tanx
tan2x
的值为______.

tan(x+

π
4
)=2,
tanx+1
1−tanx
=2,
解得tanx=
1
3

∴tan2x=
2tanx
1−tan2x
=
2
3
1−
1
9
=
3
4

tanx
tan2x
=
1
3
3
4
=
4
9

故答案为:
4
9