Найдите cos2α , если ctgα=√2 - 1 . .

Ctgα=√2-1
cos α/ sin α=√2-1
cos a=sin α*(√2-1)
cos α=√(1-cos^2 α)*(√2-1)
cos^2α=(1-cos^2 α)*(2-2√2+1)
cos^2α=(1-cos^2 α)*(3-2√2)
cos^2α(1+3-2√2)=3-2√2
cos^2 α(4-2√2)=3-2√2
cos α=√((3-2√2)/(4-2√2))
α=67.5+2p*k
cos(67.5*2)=-√2/2