(1-cos4α+sin4α)/(1+cos4α+sin4α)
=[2cos^2(2α)+2sin2αcos2α]/[2sin^2(2α)+2sin2αcos2α]
=2cos2α(sin2α+cos2α)/2sin2α(sin2α+cos2α)
=cot2α =(1-tan^2 α)/2tanα