> 数学 >
已知cos(
12
+α)=
1
3
,且-π<α<-
π
2
,则cos(
π
12
-α)=______.
人气:296 ℃ 时间:2020-01-24 11:46:56
解答
−π<α<−
π
2
12
<α+ 
12
<−
π
12

cos(
12
+α)=
1
3
sin(α+
12
)=−
2
2
3

(
12
+α)+(
π
12
−α)=
π
2

cos(
π
12
−α)=cos[
π
2
−(
12
+α)]
=sin(
12
+α)
=
2
2
3

故答案为:
2
2
3
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