（Ⅰ）∵f(x)＝[1−cos(π2+2x)]−3cos2x＝1+sin2x−3cos2x=1+2sin(2x−π3)．又∵x∈[π4，π2]，∴π6≤2x−π3≤2π3，即2≤1+2sin(2x−π3)≤3，∴f（x）max=3，f（x）min=2．（Ⅱ）∵|f（x）-m|＜2⇔f（x）-2＜...