[tex]\frac{2sin\alpha -3cos\alpha }{cos\alpha +4sin\alpha }=\frac{\frac{2sin\alpha}{cos\alpha} -\frac{3cos\alpha}{cos\alpha} }{\frac{cos\alpha}{cos\alpha} +\frac{4sin\alpha}{cos\alpha}}=\frac{2tg\alpha-3}{1+4tg\alpha}=\frac{2\cdot2-3}{1+4\cdot2}=\frac{4-3}{1+8}=\frac{1}{9}[/tex]
