f(x)=1/(tanx-cotx)
分数线上下都乘以sinx·cosx
=sinx·cosx/(sin^2 x-cos^2 x)
=2·sinx·cosx/[-2(cos^2 x-sin^2 x)]
=sin2x/[-2cos2x]
=(-1/2)·tan2x
∴最小正周期是π/2