oblicz (sin [latex] alpha [/latex]-cos[latex] alpha [/latex])[latex] ^{2}[/latex], jesli wiadomo, ze sin[latex] alpha [/latex] x cos [latex] alpha [/latex]=[latex] frac{1}{6} [/latex]

[latex]sinalpha * cosalpha = frac{1}{6}[/latex] [latex](sinalpha - cosalpha)^{2} = sin^{2}alpha - 2sinalpha cosalpha + cos^{2}alpha=\\=sin^{2}alpha + cos^{2}alpha - 2sinalpha cosalpha =\\=1 - 2*frac{1}{6}= frac{3}{3}-frac{1}{3} = frac{2}{3}[/latex]

Oblicz [latex]sin^{3} alpha +cos^3 alpha [/latex] jeśli wiadomo, że [latex]sin alpha +cos alpha = frac{2}{3} [/latex]

Oblicz [latex]sin^{3} alpha +cos^3 alpha [/latex] jeśli wiadomo, że [latex]sin alpha +cos alpha = frac{2}{3} [/latex]...