a,
$\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{5}{13}$
$\Rightarrow \tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=\dfrac{5}{12}$
$\cot\alpha=\dfrac{1}{\tan\alpha}=\dfrac{12}{5}$
b,
$\cot\alpha=\dfrac{5}{12}$
$\Rightarrow \tan\alpha=\dfrac{1}{\cot\alpha}=\dfrac{12}{5}$