[tex]cos\alpha=\frac{\sqrt{21}}{5};\ sin\alpha=\frac{2}{5}\\\\\\cos2\alpha=cos^2\alpha-sin^2\alpha\\\\cos^2\alpha=\left(\frac{\sqrt{21}}{5}\right)^2=\frac{21}{25}\\\\sin^2\alpha=\left(\frac{2}{5}\right)^2=\frac{4}{25}\\\\cos2\alpha=\frac{21}{25}-\frac{4}{25}=\frac{17}{25}[/tex]
