[tex]tg\alpha = \frac{12}{13}\\\\tg\alpha = \frac{sin\alpha}{cos\alpha}\\\\\frac{sin\alpha}{cos\alpha} = \frac{12}{13}\\\\12cos\alpha = 13sin\alpha \ \ |()^{2}\\\\144cos^{2}\alpha = 169sin^{2}\alpha\\\\sin^{2}\alpha + cos^{2}\alpha = 1\\cos^{2}\alpha = 1 - sin^{2}\alpha\\\\144(1-sin^{2}\alpha) = 169sin^{2}\alpha\\\\144-144sin^{2}\alpha=169sin^{2}\alpha\\\\313sin^{2}\alpha = 144 \ \ /:313\\\\sin^{2}\alpha = \frac{144}{313}[/tex]
[tex]sin\alpha = \frac{\sqrt{144}}{\sqrt{313}} = \frac{12}{\sqrt{313}}\cdot\frac{\sqrt{313}}{\sqrt{313}} = \frac{12\sqrt{313}}{313}[/tex]
[tex]cos^{2}\alpha = \frac{169}{144}\cdot sin^{2}\alpha =\frac{169}{144}\cdot\frac{144}{313} = \frac{169}{313}\\\\cos\alpha = \frac{\sqrt{169}}{\sqrt{313}}=\frac{13}{\sqrt{313}}\cdot\frac{\sqrt{313}}{\sqrt{313}} = \frac{13\sqrt{313}}{313}[/tex]
