sinx(1+tanx*tan2/x)
=sinx[1+(sinxsinx/2)/(cosxcosx/2)]
=sinx[sinxsinx/2+cosxcosx/2]/(cosxcosx/2)]
=sinx[cosx/2]/(cosxcosx/2)]
=sinx/cosx
=tanx
故该函数最小正周期为π.