[tex]\frac{4cos\alpha+5sin\alpha}{sin\alpha}=8\\\\\frac{4cos\alpha}{sin\alpha}+\frac{5sin\alpha}{sin\alpha}=8\\\\4ctg\alpha+5=8\\\\4ctg\alpha=8-5\\\\4ctg\alpha=3\ \ \ |:4\\\\ctg\alpha=\frac{3}{4}[/tex]
