[latex]sinalpha+cosalpha=frac{5}{4}[/latex] [latex](sinalpha+cosalpha)^2=left(frac{5}{4} ight)^2[/latex] [latex]sin^2alpha+2sinalphacosalpha+cos^2alpha=frac{25}{16}[/latex] [latex]1+2sinalphacosalpha=frac{25}{16}[/latex] [latex]2sinalphacosalpha=frac{25}{16}-1[/latex] [latex]2sinalphacosalpha=frac{9}{16}[/latex] [latex]sinalphacosalpha=frac{9}{32}[/latex] [latex](sin^2alpha+cos^2alpha)^2=sin^4alpha+2sin^2alphacos^2alpha+cos^4alpha[/latex] [latex]1=sin^4alpha+2sin^2alphacos^2alpha+cos^4alpha[/latex] [latex]1=sin^4alpha+2sin^2alphacos^2alpha+cos^4alpha[/latex] [latex]sin^4alpha+cos^4alpha=1-2(sinalphacosalpha)^2[/latex] [latex]sin^4alpha+cos^4alpha=1-2cdot left(frac{9}{32} ight)^2[/latex] [latex]sin^4alpha+cos^4alpha=1-2cdot frac{81}{1024}[/latex] [latex]sin^4alpha+cos^4alpha=1-frac{81}{512}[/latex] [latex]sin^4alpha+cos^4alpha=frac{431}{512}[/latex]
