oblicz wartosc wyrazenia 3sinα +cosα /cosα -3sinα  .... wiedziąc, że tgα =2 i α  jest kątem ostrym

[latex]tgalpha=2; tgalpha=frac{sinalpha}{cosalpha}\\frac{sinalpha}{cosalpha}=2Rightarrow sinalpha=2cosalpha\\\frac{3sinalpha+cosalpha}{cosalpha-3sinalpha}=frac{3cdot2cosalpha+cosalpha}{cosalpha-3cdot2cosalpha}=frac{6cosalpha+cosalpha}{cosalpha-6cosalpha}=frac{7cosalpha}{-5cosalpha}=-frac{7}{5}=-1frac{2}{5}[/latex] ©DRK