(1)f(x)=
[1+cos(2x-1 2
)-(1-cos2x)]=π 3
[cos(2x-1 2
)+cos2x]=cosπ 3
cos(2x-π 6
)=π 6
cos(2x-
3
2
),π 6
f(
)=π 12
cos(2×
3
2
-π 12
)=π 6
.
3
2
(2)∵x∈[0,
]π 2
∴2x-
∈[?π 6
,π 6
],∴-5π 6
3
2