Ответ:

[tex]\frac{cos\alpha}{1+sin\alpha}+tg\alpha=\frac{1}{cos\alpha}[/tex]

Объяснение:

[tex]\frac{cos\alpha}{1+sin\alpha}+\frac{sin\alpha}{cos\alpha}=\\\\\frac{cos\alpha^2}{cos\alpha(1+sin\alpha)}+\frac{sin\alpha(1+sin\alpha)}{cos\alpha(1+sin\alpha)}=\frac{cos\alpha^2+\sin\alpha(1+sin\alpha)}{cos\alpha(1+sin\alpha)}=\\\\\frac{cos\alpha^2+\sin\alpha+sin^2\alpha}{cos\alpha(1+sin\alpha)}=\frac{1+\sin\alpha}{cos\alpha(1+sin\alpha)}=\frac{1}{cos\alpha}[/tex]