1+tan^2 x

=1+sin^2x/cos^2x

=(sin^2x+cos^2x)/cos^2x

=1/cos^2x

原式

=tanx/√(1/cos^2x)

=tanx/(1/|cosx|)

=tanx|cosx|

cosx>0时

=tanxcosx

=sinx

cosx<0时

=-tanxcosx

=-sinx

x∈(-π/2,π/2)

cosx>0

f(x)=sinx

最小正周期=π