tg(π-α)-ctg(3π/2-α)=tgα-ctgα=(sinα/cosα)-(cosα/sinα)=
=(sin²α-cos²α)/(sinα*cosα)=-cos(2α)/(sinα*cosα)=
=-2*cos(2α)/(2*sinα*cosα)=-2*cos(2α)/sin(2α)=-2*ctg(2α).
tg(π-α)-ctg(3π/2-α)=tgα-ctgα=(sinα/cosα)-(cosα/sinα)=
=(sin²α-cos²α)/(sinα*cosα)=-cos(2α)/(sinα*cosα)=
=-2*cos(2α)/(2*sinα*cosα)=-2*cos(2α)/sin(2α)=-2*ctg(2α).