[tex]a) \\cos\alpha=\frac5{13}\\sin^2\alpha+cos^2\alpha=1\\sin^2\alpha+\frac{25}{169}=1\\sin^2\alpha=\frac{144}{169}\\sin\alpha=\frac{12}{13}\\\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\tg\alpha=\frac{12}{13}*\frac{13}5=\frac{12}5=2\frac25\\\\ctg\alpha=\frac{1}{tg\alpha}=1:\frac{sin\alpha}{cos\alpha}=\frac{cos\alpha}{sin\alpha}\\ctg\alpha=\frac5{13}*\frac{13}{12}=\frac5{12}[/tex]
[tex]b)\\tg\alpha=\frac8{15}\\tg^2\alpha=\frac{sin^2\alpha}{cos^2\alpha}\\tg^2\alpha=\frac{1-cos^2\alpha}{cos^2\alpha}\\\frac{64}{225}=\frac{1-cos^2\alpha}{cos^2\alpha}\\225(1-cos^2\alpha)=64cos^2\alpha\\225-225cos^2\alpha=64cos^2\alpha/ +225cos^2\alpha\\225=289cos^2\alpha /:289\\cos^2\alpha=\frac{225}{289}\\cos\alpha=\sqrt{\frac{225}{289}}=\frac{15}{17}\\\\sin^2\alpha=1-\frac{225}{289}\\sin^2\alpha=\frac{64}{289}\\sin\alpha=\frac8{17}\\ctg\alpha=\frac{15}8=1\frac78[/tex]