[tex]tg\alpha=2\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\tg^2\alpha=\frac{sin^2\alpha}{cos^2\alpha}\\sin^2\alpha+cos^2\alpha=1\\sin^2\alpha=1-cos^2\alpha\\\\tg^2\alpha=\frac{1-cos^2\alpha}{cos^2\alpha}\\2^2=\frac{1-cos^2\alpha}{cos^2\alpha}\\4cos^2\alpha=1-cos^2\alpha /+cos^2\alpha\\[/tex]
[tex]5cos^2\alpha=1 /:5\\cos^2\alpha=\frac15\\cos\alpha=\frac{1}{\sqrt5}=\frac{\sqrt5}5\\\\sin^2\alpha=1-\frac15\\sin^2\alpha=\frac45\\sin\alpha=\frac{2}{\sqrt5}=\frac{2\sqrt5}5\\\\ctg\alpha=\frac{1}{tg\alpha}\\ctg\alpha=\frac12[/tex]
