问题 填空题
已知sin(
π
4
-α)=
1
3
,则
(1-cos2α)cos(
π
4
+α)
(1+cos2α)•tan2α
=______.
答案

∵sin(

π
4
-α)=
1
3
,∴cos(
π
4
+α)=sin[
π
2
-(
π
4
+α)]
=sin(
π
4
-α)=
1
3

(1-cos2α)cos(
π
4
+α)
(1+cos2α)•tan2α
=
2sin2α×
1
3
2cos2α•tan2α
=
1
3
×
sin2α
sin2α
=
1
3

故答案为

1
3

选择题
单项选择题