Упростите: Ответ

Решите задачу:

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