ДАЮ 90 БАЛЛОВ !!!!! Докажите тождество

[latex]ctg\alpha-tg\alpha={cos^2\alpha-sin^2\alpha\over cos\alpha sin\alpha}=2ctg{2\alpha}\\\\{1\over2}sin4\alpha=sin2\alpha cos2\alpha\\\\2ctg{2\alpha}*sin2\alpha cos2\alpha=2cos^22\alpha\\\\cos^4\alpha+1=2cos^2\alpha-1+1=2cos^22\alpha[/latex]