2sin2(π/4+x)-（根號)3cos2x
=2sin(π/2+2x)-根號3cos2x
=2sin[π-(π/2-2x)]-根號3cos2x
=2sin(π/2-2x)-根號3cos2x
=2cos2x-根號3cos2x
=(2-根號3)cos2x
-1≤cos2x≤1
（根號3-2）≤(2-根號3)cos2x≤（2-根號3）
最小值：根號3-2
最大值：2-根號3
【備注:如果原題是：2sin平方[(π/4)+x]-(根號3)cos2x】
則原式=[1-cos[2(π/4)+x)]-(根號3)cos2x
=1-cos(π/2+2x)-(根號3)cos2x
=1+sin2x-(根號3)cos2x
=1+2{1/2sin2x-[(根號3)/2]cos2x}
=1+2[sin2xcos(π/3)-cos2xsin(π/3)]
=1+2sin(2x-π/3)
-1≤sin(2x-π/3)≤1
-1≤1+2sin(2x-π/3)≤3
最小值：-1
最大值：3