[latex]ctg2alpha=3\ frac{ctg^{2}alpha-1}{2ctgalpha}=3\ frac{frac{cos^{2}alpha}{sin^{2}alpha}-1}{frac{2cosalpha}{sinalpha}}=3\ frac{cos^{2}alpha-sin^{2}alpha}{sin^{2}alpha}*frac{sinalpha}{2cosalpha}=3\ [/latex] [latex]frac{cos^{2}alpha-sin^{2}alpha}{2sinalpha cosalpha}=3\ cos^{2}alpha-sin^{2}alpha=6sinalpha cosalpha\ sinalpha cosalpha=frac{cos^{2}-sin^{2}}{6}[/latex] Podstawiamy za [latex]sinalpha cosalpha[/latex] w wyjsciowej formule do obliczenia. [latex]frac{frac{cos^{2}alpha-sin^{2}alpha}{6}}{sin^{2}alpha-cos^{2}alpha}=frac{cos^{2}alpha-sin^{2}alpha}{6}*frac{1}{sin^{2}alpha-cos^{2}alpha}[/latex] [latex]frac{1-sin^{2}alpha-sin^{2}alpha}{6[sin^{2}alpha-(1-sin^{2}alpha)]}=frac{1-2sin^{2}alpha}{-6(-2sin^{2}+1)}=frac{-1}{6}[/latex]
