1)(cos²π/8-sin²π/8)²=(cos2·π/8)²=(cosπ/4)²=(√2/2)²=2/4=0,5
2)(2sinα-sin2α)/(cosα-1+sin²α)=(2sinα-2sinαcosα)/(cosα-sin²α-cos²α+sin²α)=
2sinα(1-cosα)/cosα(1-cosα)=2sinα/cosα=2tgα
1+sin(π+α)cos(α+3π/2)-cos²α=sin²α+cos²α-sinαsinα-cos²α=0
3)[sin(π-3α)-cos(π/2+α)]/[sin(3π/2+α)+cos3α]=(sin3α+sinα)/(-cosα+cos3α)=
2sin2αcosα/-2sinαsin2α=-cosα/sinα=-ctgα