y=tanx+cotx
=sinx/cosx+cosx/sinx
=(sinx^2+cosx^2)/sinxcosx
=1/sinxcosx
=2/sin2x
y=tanx-cotx
=sinx/cosx-cosx/sinx
=(sinx^2-cosx^2)/sinxcosx
=-2cos2x/sin2x
=-2cot2x