问题 解答题
已知cos(α+
π
4
)=
3
5
π
2
≤α<
2
,求cos(2α+
π
4
)
的值.
答案

cos(2α+

π
4
)=cos2αcos
π
4
-sin2αsin
π
4
=
2
2
(cos2α-sin2α).
4
≤α+
4
且cos(α+
π
4
)>0
4
≤α+
π
4
4

sin(α+

π
4
)=-
1-cos2(α+
π
4
)
=-
4
5

从而cos2α=sin(2α+

π
2
)=2sin(α+
π
4
)cos(α+
π
4
)=-
24
25

sin2α=-cos(2α+

π
2
)=1-2cos2(α+
π
4
)=
7
25

cos(2α+

π
4
)=
2
2
×(-
24
25
-
7
25
)=-
31
2
50

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