\cos 2x &amp; = 2 \cos^2 x - 1 \\\cos 2x &amp;= 2 \left (- \frac{13}{14} \right )^2 - 1 \\\cos 2x &amp;= 2 \left (\frac{169}{196} \right )-1 \\\cos 2x &amp; = \left (\frac{338}{196} \right )-1 \\\cos 2x &amp;=  \frac{338}{196} - \frac{196}{196} \\\cos 2x &amp;= \frac{142}{196} = \frac{71}{98}