Ctgα-tgα=(cosα/sinα)-(sinα/cosα)=(cos²α-sin²α)/(sinα*cosα)=
=2*cos(2α)/(2*sinα*cosα)=2*cos(2α)/sin(2α).
tgα+ctgα=(sinα/cosα)+(cosα/sinα)=(sin²α+cos²α)/(sinα*cosα)=
=2*1/(2*sinα*cosα)=2/sin(2α)=√8
sin(2α)=2/√8=2√8/8=√8/4=2√2/4=√2/2
sin²(2α)=(√2/2)²=2/4=1/2
cos²(2α)=1-sin²(2α)=1-1/2=1/2
cos(2α)=√(1/2)=1/√2=√2/2 ⇒
ctgx-tgx=2*(√2/2)/(√2/2)=2.
Ответ: б) 2.