[latex]tgalpha=frac{sinalpha}{cosalpha} [/latex] [latex]tgalpha+frac{1}{tgalpha}=frac{sinalpha}{cosal}+frac{cosal}{sinal}[/latex]= [latex]frac{sin^{2}al+cos^{2}al}{sinal*cosal}=frac{1}{sinal*cosal}[/latex] [latex](frac{1}{sinal*cosal})^{2}=frac{1}{sin^{2}al*cos^{2}al}=frac{1}{(1-cos^{2}al)*cos^{2}al}[/latex] skorzystalem tutaj z jedynki trygonometrycznej :) [latex]cosal=frac{1}{2} [/latex] zatem [latex]cos^{2}al=frac{1}{4}[/latex] kwintesencje zadania zostawiamTobie, wystarcz jedną czwartą wstawic do wzoru i wyliczyc :) powodzenia :)
[latex]tg alpha=frac{sin alpha}{cos alpha}\ left(frac{sin alpha}{cos alpha}+frac{1}{frac{sin alpha}{cos alpha}} ight)^{2}=[/latex] [latex]=left(frac{sin alpha}{cos alpha}+frac{cos alpha}{sin alpha} ight)^{2}= left(frac{sin^{2} alpha}{cos alpha cdot sin alpha}+frac{cos^{2} alpha }{sin alpha cdot cosalpha} ight)^{2}=[/latex] [latex]= left(frac{1}{cos alpha cdot sin alpha} ight)^{2}=frac{1}{cos^{2}alpha cdot sin^{2}alpha}= frac{1}{cos^{2} alpha (1- cos^{2}alpha)}[/latex] [latex] cos alpha=frac{1}{2}\ frac{1}{cos^{2} alpha (1- cos^{2}alpha)}=frac{1}{left(frac{1}{2} ight)^{2} cdot left(1-left(frac{1}{2} ight)^{2} ight)}=[/latex] [latex]frac{1}{frac{1}{4} cdot frac{3}{4}}=frac{1}{frac{3}{16}}=frac{16}{3}=5frac{1}{3}[/latex]
