已知
(1)求函数f(x)的单调增区间; (2)若f(x)=
|
(1)∵f(x)=
•a
=2sin(x+b
)-2cosx=2sinxcosπ 6
+2cosxsinπ 6
-2cosx π 6
=
sinx-cosx=2sin(x-3
) …(5分)π 6
由-
+2kπ≤x-π 2
≤π 6
+2kπ,k∈z,得,-π 2
+2kπ≤x≤π 3
+2kπ. …(7分)2π 3
故函数f(x)的单调增区间为[-
+2kπ , π 3
+2kπ],k∈z.…(8分)2π 3
(2)由(1)可得f(x)=
即 sin(x-6 5
)=π 6
.…(10分)3 5
∴cos(2x-
)=1-2sin2(x-π 3
)=π 6
.…(12分)7 25