tg\alpha =0,9=\frac{9}{10}
ctg\alpha=\frac{1}{tg\alpha}=\frac{10}{9}=1\frac{1}{9}
\frac{sin^2\alpha}{cos^2\alpha}=tg^2\alpha
\frac{1-cos^2\alpha}{cos^2\alpha}=(\frac{9}{10})^2
\frac{1-cos^2\alpha}{cos^2\alpha}=\frac{81}{100}
100(1-cos^2\alpha)=81cos^2\alpha
100-100cos^2\alpha=81cos^2\alpha
100cos^2\alpha+81cos^2\alpha=100
181cos^2\alpha=100
cos^2\alpha=\frac{100}{181}
cos\alpha=\sqrt{\frac{100}{181}}=\frac{10}{\sqrt{181}}
sin^2\alpha=1-cos^2\alpha=1-\frac{100}{181}=\frac{81}{181}
sin\alpha=\sqrt{\frac{81}{181}}=\frac{9}{\sqrt{181}}