2sin^2(π/4+x)可以化为1-COS(π/2+2X)
故原式可化为:f(x)=1-COS(π/2+2X)-√3cos2x 即:f(x)=1-[COS(π/2+2X)+√3cos2x ]
=1-(SIN2X+√3cos2x)
=1-2*SIN(2X+π/3)
故:1.f(x)的最小正周期为:2π/2的绝对值=π
2.要求f(x)单调减区间,需求SIN(2X+π/3)的单调增区间,即令:2Kπ-π/2