(sinα-cosα)·√2/√2=√2(1/√2·sinα-1/√2cosα)=-√2(cosπ/4cosα-sinπ/4sinα)=
=-√2cos(π/4+α)
(sinα-2sin2α+sin3α)/(cosα-2cos2α+cos3α)=((sinα+sin3α)-2sin2α)/(cosα+cos3α-2cos2α)=
=(2sin2α·cos(-α)-2sin2α)/(2cos2α·cos(-α)-2cos2α)=(2sin2α)(cosα-1)/(2cos2α)(cosα-1)=
=2sin2α/2cos2α=tg2α