Zad.1 Oblicz sin beta,cos beta,ctg beta, wiedząc,że tg beta=-5/12 Zad.2 Uzasadnij tożsamość: a) cos^2 alfa=ctg alfa/tg alfa+ctg alfa b)tg alfa*ctg alfa/1-sin^2 alfa=tg^2+1

1. [latex]tgeta = -frac{5}{12}\ctgeta = -frac{12}{5} = frac{coseta}{sineta}\coseta = -frac{12}{5}sineta\(-frac{12}{5}sineta)^{2}+sin^{2}eta=1\frac{144}{25}sin^{2}eta+sin^{2}eta = 1\sin^{2}eta = frac{25}{169}\sineta = frac{5}{13}\\coseta = -frac{12}{5}*frac{5}{13} =- frac{12}{13}[/latex]   2. [latex]P = frac{frac{cosalpha}{sinalpha}}{frac{cosalpha}{sinalpha}+frac{sinalpha}{cosalpha}} = frac{frac{cosalpha}{sinalpha}}{frac{1}{sinalpha}}{cosalpha} = frac{cosalpha}{sinalpha}*sinalpha cosalpha = cos^{2}alpha[/latex]   3. [latex]P = tg^{2}alpha + 1 = frac{sin^{2}alpha}{cos^{2}alpha}+frac{cos^{2}alpha}{cos^{2}alpha} = frac{1}{cos^{2}alpha} = frac{tgalpha*ctgalpha}{1-sin^{2}alpha}[/latex]