oblicz możliwe wartości wyrażenia sinα −cos α wiedząc że sinαcosα=0.25

  [latex]sinalpha cos alpha =0,25 \ - sinalpha cos alpha = -0,25\ -2sinalpha cos alpha = -0,5\ 1-2sinalpha cosalpha = 1-0,5\ sin^2 alpha + cos^2 alpha - 2sinalpha cosalpha = 0,5\ (sinalpha - cosalpha)^2 = frac{1}{2}\ sinalpha- cosalpha = sqrt{frac{1}{2}} = frac{1}{sqrt2} = frac{sqrt2}{2} [/latex] [latex]sinalpha - cosalpha = -frac{sqrt2}{2}[/latex]