[tex] \frac{4cos \: a + 5sin \: a }{sin \: a} = \frac{4cos \: a}{sin \: a} + \frac{5sina}{sin \: a} = 4ctg \: a + 5 \\ 4ctg \: a + 5 = 8 \: | - 5 \\ 4ctg \: a = 3 | \div 4 \\ ctg \: a = \frac{3}{4} \\ \frac{1}{tg \: a} = \frac{3}{4} | \times 4tg \: a \\ 4 = 3tg \: a | \div 3\\ \frac{4}{3} = tg \: a[/tex]