Oblicz wartość wyrażenia 3cos alfa - 2sin alfa / sin alfa - 5 cos alfa jeśli wiadomo za alfa jest katem ostrym tg alfa = 2/5

[latex]tgalpha = frac{2}{5}\\frac{sinalpha}{cosalpha} = tgalpha\\frac{sinalpha}{cosalpha} = frac{2}{5}\\2cosalpha = 5sinalpha /:2\\cosalpha = frac{5}{2}sinalpha[/latex] [latex]frac{3cosalpha-2sinalpha}{sinalpha - 5cosalpha} = frac{3*frac{5}{2}sinalpha-2sinalpha}{sinalpha - 5*frac{5}{2}sinalpha}=frac{sinalpha(frac{15}{2}-frac{4}{2})}{siinalpha(frac{2}{2}-frac{25}{2})}=frac{frac{11}{2}}{frac{-23}2}}=-frac{11}{23}[/latex]