Option B: $\dfrac{4}{\sqrt{3}}$
$2\sin A = 1 \Rightarrow \sin A = \dfrac{1}{2} \Rightarrow A = 30°$
$\tan 30° + \cot 30° = \dfrac{1}{\sqrt{3}} + \sqrt{3} = \dfrac{1+3}{\sqrt{3}} = \dfrac{4}{\sqrt{3}}$
Find A from the given condition, then substitute standard values. Key standard values to remember: $\tan 30° = \frac{1}{\sqrt{3}}$, $\cot 30° = \sqrt{3}$. Adding them over a common denominator gives $\frac{4}{\sqrt{3}}$. Always simplify to a single fraction to match the option exactly.