Oblicz wartość wyrażenia [latex] frac{4 sin alpha - 5cos alpha }{cos alpha + 3sin alpha }[/latex] gdy ctgα = -2

[latex]ctgalpha=frac{cosalpha}{sinalpha}=-2\cosalpha=-2sinalpha[/latex] [latex]frac{4sinalpha-5cosalpha}{cosalpha+3sinalpha}=frac{4sinalpha+10sinalpha}{-2sinalpha+3sinalpha}=frac{14sinalpha}{sinalpha}=14[/latex]