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

∵sin(x+

π
6
)=
1
4

∴cos2(x+

π
6
)=1-sin2(x+
π
6
)=
15
16

则sin(

6
+x)+cos2
6
-x)

=sin[π+(x+

π
6
)]+cos2[π-(x+
π
6
)]

=-sin(x+

π
6
)+cos2(x+
π
6

=-

1
4
+
15
16

=

7
8

故答案为:

7
8

填空题
填空题