f《x》=《sinx+cosx》sinx 求最小正周期是?

f(x)=(sinx+cosx)sinx
=(sinx)^2+sinxcosx
=(1-cos2x)/2+(1/2)sin2x
=(1/2)(sin2x-cos2x)+1/2
=[(根号2)/2]sin(2x+pi/4)+1/2
故它的周期为2pi/2=pi