Докажите тождество 2sin^2(α)/tg2α*tgα=cos^2(α)-sin^2(α)

Question

Докажите тождество 2sin^2(α)/tg2α*tgα=cos^2(α)-sin^2(α)

Answer 1

cos^2(α)-sin^2(α)=cos(2a)

2sin^2(α)/tg2α*tgα=(2sina*cosa)/tg2a=sin2a*cos2a/sin2a=cos2a