Помогите с алгеброй пже, 304(а); 306

Решите задачу:

$( \frac{1}{1+Ctg ^{2} \alpha}+Cos ^{2} \alpha )*tg ^{2} \alpha =( \frac{1}{ \frac{1}{Sin ^{2} \alpha } } +Cos ^{2} \alpha)*tg ^{2} \alpha =$ $(Sin ^{2} \alpha +Cos ^{2} \alpha )*tg ^{2} \alpha =1*tg ^{2} \alpha =tg ^{2} \alpha$

$1+tg ^{2} \alpha = \frac{1}{Cos ^{2} \alpha }\\\\tg ^{2} \alpha = \frac{1}{ \frac{4}{5} } -1= \frac{5}{4} -1= \frac{1}{4} \\\\tg \alpha = \frac{1}{2}$