Jeżeli sin alfa + cos alfa = pierwiastek z 2 to ile wynosi iloczyn sin alfa razy cos alfa?

[latex]sin^2alpha+2sinalpha cosalpha +cos^2alpha=2\2sinalpha cosalpha=1\sinalpha cosalpha ={1over 2}[/latex]

[latex]sinalpha+cosalpha=sqrt2\ (sinalpha+cosalpha)^2=(sqrt2)^2\ underbrace{sin^2alpha+cos^2alpha}_1+2sinalphacdotcosalpha=2\ 1+2sinalpha+cosalpha=2\ 2sinalphacdotcosalpha=1\ oxed{sinalphacdotcosalpha=frac12}[/latex]