correcting the typo ...
$\displaystyle \cos{t} = -\frac{7}{25}$ , $\displaystyle \sin{t} = \frac{24}{25}$
$\displaystyle \tan(2t) = \frac{\sin(2t)}{\cos(2t)} = \frac{2\sin{t}\cos{t}}{2\cos^2{t} - 1}$
sub in the values for sine and cosine yields
$\displaystyle \tan(2t) = \frac{336}{527}$