ОТДАЮ ПОСЛЕДНИЕ БАЛЛЫУпростите выражение (2+tg^2α+ctg^2α)*tg^2α

Решите задачу:

$(2+tg^2\alpha +ctg^2\alpha)tg^2\alpha= (2+\frac{sin^2\alpha}{cos^2\alpha}+\frac{cos^2\alpha}{sin^2\alpha})tg^2\alpha= \\\ =(2+\frac{sin^4 \alpha+cos^4\alpha}{sin^2\alpha cos^2\alpha})tg^2\alpha = \frac{sin^4\alpha+cos^4\alpha+2sin^2\alpha cos^2\alpha}{sin^2\alpha cos^2 \alpha }\cdot tg^2 \alpha= \\\ =\frac{(sin^2 \alpha+cos^2\alpha)^2}{sin^2\alpha cos^2\alpha}\cdot\frac{sin^2\alpha}{cos^2\alpha}=\frac{1}{sin^2\alpha cos^2\alpha}\cdot\frac{sin^2\alpha}{cos^2\alpha}=\frac{1}{cos^4\alpha}$