问题 解答题
已知cos(
π
4
+x)=
3
5
,且0<x<
π
4
,求
sin(
π
4
-x)
cos(2x+5π)
+sin(2x-
2
)
的值.
答案

因为cos(

π
4
+x)=
3
5
,且0<x<
π
4

所以:sin(x+

π
4
)=
4
5

所以:

sin(
π
4
-x)
cos(2x+5π)
+sin(2x-
2
)

=

cos(x+
π
4
)
-cos2x
+sin(2x+
π
2

=-

cos(x+
π
4
)
sin(2x+
π
2
)
+sin(2x+
π
2

=-

cos(x+
π
4
)
2sin(x+
π
4
)cos(x+
π
4
)
+2sin(x+
π
4
)cos(x+
π
4

=-

3
5
3
5
×
4
5
+2×
3
5
×
4
5

=-

5
8
+
24
25

=

67
200

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