[tex](cos\alpha+tg\alpha\cdot sin\akpha)\cdot ctg\alpha = cos\alpha \cdot ctg\alpha + tg\alpha\cdot ctg\alpha\cdot sin\alpha = cos\alpha \cdot\frac{cos\alpha}{sina\alpha}+1\cdot sin\alpha=\\\\=\frac{cos^{2}\alpha}{sin\alpha} + sin\alpha = \frac{cos^{2}\alpha + sin^{2}\alpha}{sin\alpha} = \frac{1}{sin\alpha}\\\\\boxed{Odp. \ A.}[/tex]
Wyjaśnienie:
[tex]ctg\alpha = \frac{cos\alpha}{sin\alpha}\\\\tg\alpha \cdot ctg\alpha = 1\\\\sin^{2}\alpha + cos^{2}\alpha = 1[/tex]
