[tex]sin=\frac25\\\\sin^2\alpha+cos^2\alpha=1\\(\frac25)^2+cos^2\alpha=1\\\frac4{25}+cos^2\alpha=1\\cos^2\alpha=1-\frac4{25}\\cos^2\alpha=\frac{21}{25}\\cos\alpha=\frac{\sqrt{21}}5\\\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\tg\alpha=\frac25*\frac{5}{\sqrt{21}}=\frac{2}{\sqrt{21}}=\frac{2\sqrt{21}}{21}\\\\tg\alpha*ctg\alpha=1\\\frac{2\sqrt{21}}{21}*ctg\alpha=1 /*\frac{21}{2\sqrt{21}}\\ctg\alpha=\frac{21}{2\sqrt{21}}=\frac{21\sqrt{21}}{2*21}=\frac{\sqrt{21}}2[/tex]
