已知函数f(x)＝2cosxsin(x+π3)−3sin2x+sinxcosx

（Ⅰ）f(x)＝2cosx(
1
2sinx+

3
2cosx)−
3sin2x+sinxcosx
=2sinxcosx+
3(cos2x−sin2x)
=sin2x+
3cos2x
=2sin(2x+
π
3)
∴T=π
（Ⅱ）f（x）的减区间为2kπ+
π
2≤2x+
π
3≤2kπ+
3π
2，kπ+
π
12≤x≤kπ+
7π
12
又∵x∈[−
π
2，−
π
12]，∴−
π
2≤x≤−
5π
12或
π
12≤x≤
π
2
即f（x）在[−
π
2，−
5π
12]和在[
π
12，
π
2]上单调递减．