sin²a+cos²a=1 a) sin a = 1/10 (1/10)²+cos²a=1 1/100+cos²a=1 cos²a= 99/100 cos a= [latex]frac{3sqrt{11}}{10} \ tgalpha= frac{sinalpha}{cosalpha}\ tgalpha=frac{frac{1}{10}}{frac{3sqrt{11}}{10}}\ tgalpha= frac{1}{3sqrt{11}}\ tgalpha= frac{3sqrt{11}}{99}\ tgalpha= frac{sqrt{11}}{33}\ ctgalpha= frac{cosalpha}{sinalpha}\ ctgalpha= frac{frac{3sqrt{11}}{10}}{frac{1}{10}} \ ctgalpha= 3sqrt{11}[/latex] b) [latex]tgalha= sqrt{5}\ tgalpha*ctgalpha=1\ sqrt{5}*ctgalpha=1\ ctgalpha= frac{1}{sqrt{5}}\ ctgalpha= frac{sqrt{5}}{5}\ tgalpha= frac{sinalpha}{cosalpha}\ sqrt{5}= frac{sinalpha}{cosalpha}\ sqrt{5}cosalpha= sinalpha\ sin^alpha+cos^2alpha=1\ (sqrt{5}cosalpha)^2+cos^2alpha=1 \ 5cos^2alpha+cos^2alpha=1\ 6cos^2alpha= 1\ cos^2alpha= frac{1}{6}\ cosalpha= frac{sqrt{6}}{6}\ sinalpha= sqrt{5}*frac{sqrt{6}}{6}\ sinalpha= frac{sqrt{30}}{6}\ Licze na naj :)[/latex]
