[latex]sinalpha + cosalpha = frac{7}{5} \\ 0^o extless alpha extless 90^o o sinalpha extgreater 0 wedge cosalpha extgreater 0[/latex] [latex]sinalpha + cosalpha = frac{7}{5} /^2 \\ (sinalpha + cosalpha)^2 = (frac{7}{5})^2 \\ sin^2alpha+ 2 cdot sinalpha cdot cosalpha + cos^2alpha = frac{49}{25} \\ underbrace{sin^2alpha+cos^2alpha}_{=1} + 2 cdot sinalpha cdot cosalpha = frac{49}{25} \\ 1 +2 cdot sinalpha cdot cosalpha = frac{49}{25} \\ 2 cdot sinalpha cdot cosalpha = frac{49}{25} - 1[/latex] [latex]2 cdot sinalpha cdot cosalpha = frac{49}{25} - frac{25}{25} \\ 2 cdot sinalpha cdot cosalpha = frac{24}{25}[/latex] [latex](sinalpha - cosalpha)^2 = sin^2alpha - 2 cdot sinalpha cdot cosalpha + cos^2alpha =\\ =underbrace{sin^2alpha+cos^2alpha}_{=1} - 2 cdot sinalpha cdot cosalpha = 1 -2 cdot sinalpha cdot cosalpha = \\ =1- frac{24}{25} = frac{25}{25} -frac{24}{25} =frac{1}{25}[/latex] Stąd: [latex](sinalpha - cosalpha)^2 =frac{1}{25} \\ sinalpha - cosalpha=frac{1}{5} vee sinalpha - cosalpha=-frac{1}{5}[/latex] 1⁰ [latex]sinalpha - cosalpha=frac{1}{5} \\ sin^2alpha - cos^2alpha = (sinalpha - cosalpha)(sinalpha + cosalpha) = frac{1}{5} cdot frac{7}{5} = frac{7}{25}[/latex] 2⁰ [latex]sinalpha - cosalpha=-frac{1}{5} \\ sin^2alpha - cos^2alpha = (sinalpha - cosalpha)(sinalpha + cosalpha) = -frac{1}{5} cdot frac{7}{5} = -frac{7}{25}[/latex] Odp. Wartość liczbowa wyrażenia wynosi [latex]frac{7}{25} lub -frac{7}{25}[/latex]
