问题 填空题
已知sin(x+
π
6
)=
1
4
,则sin(
6
-x)+cos2(
π
3
-x)
=______.
答案

sin(x+

π
6
)=
1
4

sin(

6
-x)+cos2(
π
3
-x)

=sin[π-(x+

π
6
)]+cos2[
π
2
-(x+
π
6
)]

=sin(x+

π
6
)+sin2(x+
π
6
)

=

1
4
+
1
16

=

5
16

故答案为:

5
16

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