[tex]ctg\alpha=\frac73\\\\tg\alpha*ctg\alpha=1\\tg\alpha * \frac73 = 1 /*\frac37\\tg\alpha=\frac37[/tex]
[tex]tg\alpha=\frac{sin\alpha}{cos\alpha}\\(tg\alpha)^2=(\frac{sin\alpha}{cos\alpha})^2\\tg^2\alpha=\frac{sin^2\alpha}{cos^2\alpha}\\\\sin^2\alpha+cos^2\alpha=1\\sin^2\alpha=1-cos^2\alpha\\\\(\frac37)^2=\frac{1-cos^2\alpha}{cos^2\alpha}\\\frac9{49}=\frac{1-cos^2\alpha}{cos^2\alpha}\\\\9cos^2\alpha=49(1-cos^2\alpha)\\9cos^2\alpha=49-49cos^2\alpha /+49cos^2\alpha\\58cos^2\alpha=49 /:58\\cos^2\alpha=\frac{49}{58}\\cos\alpha=\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}\\\\[/tex]
[tex]sin^2\alpha=1-\frac{49}{58}\\sin^2\alpha=\frac{9}{58}\\sin\alpha=\frac3{\sqrt{58}}=\frac{3\sqrt{58}}{58}[/tex]
