f(x)=cos(2x+π\3)+sin^2x
=1/2cos2x-√3/2*sin2x+1-1/2(1+cos2x)
=-√3/2*sin2x+1/2
2x∈[2k∏+∏/2,2k∏+3∏/2]
即x∈[k∏+∏/4,k∏+3∏/4]
函数f(x)的单调递增