(1)(sin2α-cos2α)^2=sin2α^2+cos2α^2-2sin2αcos2α=1-sin4α;
(3) 2tanx=4tanx/2/(1-tanx/2^2)
tan(x/2+π/4)+tan(x/2-π/4)=(tanx/2+1)/(1-tanx/2)+(tanx/2-1)/(1+tanx/2)
=4tanx/2/(1-tanx/2^2);
(5) (1-2sinαcosα)/(cosα^2-sinα^2)=(sinα^2+cosα^2-2sinαcosα)/(cosα^2-sinα^2)
=(cosα-sinα)^2/(cosα-sinα)(cosα+sinα)=cosα-sinα/cosα+sinα
=(1-sinα/cosα)/(1+sinα/cosα)/=(1-tanα)/(1+tanα);
(7)(1-cos2θ)/(1+cos2θ)={1-(2cosθ^2-1)}/{1+(2cosθ^2-1)}=(2-2cosθ^2)/2cosθ^2
=2sinθ^2/2cosθ^2=tanθ^2