Найдите tgα,если cosα=2√5/5 и α € (3π/2; 2π). : )

Tg^2α+1=1/cos^2α
tg^2α=1/cos^2α - 1
tg^2α=(1-cos^2α)/cos^2α  α € (3π/2;2π) tg<0
tgα=-√(1-cos^2α)/cos^2α)=-√(1-(2√5/5)^2/ (2√5/5)^2)=-√(1-4/5)/4/5=-√(1/5*5/4)=-√1/4 =-1/2