[latex]frac{sqrt{2}cos^2alpha - sqrt{2}sin^2alpha}{4cos^2alpha - 3sin^2alpha}[/latex] [latex]tgalpha = frac{sqrt{2}}{3}[/latex] Wyciągamy przed nawias wspólny czynnik w liczniku: [latex]frac{sqrt{2}(cos^2alpha - sin^2alpha)}{4cos^2alpha - 3sin^2alpha}[/latex] W liczniku i mianowniku wyciągamy przed nawias cos²α: [latex]frac{sqrt{2}cos^2alpha(1- sin^2alpha)}{cos^2alpha(4 - 3frac{sin^2alpha}{cos^2alpha})}[/latex] Skracamy cos²α i stosujemy jedynkę trygonometryczną: [latex]sin^2alpha + cos^2alpha = 1\ cos^2alpha = 1 - sin^2alpha[/latex] [latex]frac{sqrt{2}cos^2alpha}{4 - 3(frac{sinalpha}{cosalpha})^2}[/latex] Stosujemy wzór: [latex]frac{sinalpha}{cosalpha} = tgalpha[/latex] [latex]frac{sqrt{2}cos^2alpha}{4 - 3tg^2alpha)}[/latex] Podstawiamy wartość tangensa: [latex]frac{sqrt{2}cos^2alpha}{4 - 3*(frac{sqrt{2}}{3})^2}[/latex] [latex]frac{sqrt{2}cos^2alpha}{4 - 3*frac{2}{9}}[/latex] [latex]frac{sqrt{2}cos^2alpha}{4 - frac{2}{3}}[/latex] [latex]frac{sqrt{2}cos^2alpha}{3frac{1}{3}}[/latex] [latex]frac{sqrt{2}cos^2alpha}{frac{10}{3}}[/latex] [latex]sqrt{2}cos^2alpha*frac{3}{10}[/latex] [latex]frac{3sqrt{2}}{10}cos^2alpha[/latex]
