已知tanθ=1/3,则cos2θ+1/2sin2θ= _ .

问题描述:

已知tanθ=

1
3
,则cos2θ+
1
2
sin2θ= ___ .

∵tanθ=

1
3

∴cos2θ+
1
2
sin2θ=
cos2θ+sinθcosθ
cos2θ+sin2θ
=
1+tanθ
1+tan2θ
=
1+
1
3
1+
1
9
=
6
5

故答案为:
6
5