问题
解答题
已知cos(α+
|
答案
cos(2α+
)=cos2αcosπ 4
-sin2αsinπ 4
=π 4
(cos2α-sin2α).2 2
≤α+3π 4
且cos(α+7π 4
)＞0，π 4
≤α+3π 4
＜π 4
，7π 4
∴sin(α+
)=-π 4
=-1-cos2(α+
)π 4 4 5
从而cos2α=sin(2α+
)=2sin(α+π 2
)cos(α+π 4
)=-π 4
，24 25
sin2α=-cos(2α+
)=1-2cos2(α+π 2
)=π 4 7 25
∴cos(2α+
)=π 4
×(-2 2
-24 25
)=-7 25 31 2 50