f(x)=cosx(sinx+cosx)
=sinxcosx+cos²x
=1/2sin2x+1/2(1+cos2x)
=1/2sin2x+1/2cos2x+1/2
=√2/2(√2/2sin2x+√2/2cos2x)+1/2
=√2/2sin(2x+π/4)+1/2
f(x)的最小正周期为T=2π/2=π