已知a=(cosπ2,32-cosπ2),b=(32+cosx2,sinx2)且a∥b.求1+2cos(2x-π4)sin(x+π2)的值.-数学

题目简介

已知a=(cosπ2,32-cosπ2),b=(32+cosx2,sinx2)且a∥b.求1+2cos(2x-π4)sin(x+π2)的值.-数学

题目详情

已知
a
=(cos
π
2
3
2
-cos
π
2
),
b
=(
3
2
+cos
x
2
,sin
x
2
)且
a
b
.求
1+
2
cos(2x-
π
4
)
sin(x+
π
2
)
的值.
题型:解答题难度:中档来源:不详

答案

a
b
 得,class="stub"3
4
-cos2class="stub"x
2
-sinclass="stub"x
2
cosclass="stub"x
2
=0

class="stub"3
4
-class="stub"1+cosx
2
-class="stub"1
2
sinx=0, ∴sinx+cosx=class="stub"1
2

1+
2
cos(2x-class="stub"π
4
)
sin(x+class="stub"π
2
)
=
1+
2
(cos2xcosclass="stub"π
4
+sin2xsinclass="stub"π
4
)
cos x
=class="stub"1+cos2x+sin2x
cosx
=
2cos2x+2sin xcosx
cos x
=2(sinx+cosx)=1

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