Answer
$\dfrac{2 \sqrt 3}{3}$
Work Step by Step
We need to compute $\sec 30^{\circ} \cot 45^{\circ}$.
Note that $\sec x=\dfrac{1}{\cos x}$ and $\cot x=\dfrac{1}{\tan x}$.
Since $\cos{30^{\circ}}=\frac{\sqrt3}{2}$ nd $\tan{45^{\circ}}=1$, then $\sec{30^{\circ}}=\dfrac{1}{\frac{\sqrt3}{2}}=\dfrac{2\sqrt3}{3}$ and $\cot{45^{\circ}}=1$ .
Thus,
$\sec 30^{\circ} \cot 45^{\circ} \\
=\dfrac{2\sqrt 3}{3} \times 1 \\
=\dfrac{2 \sqrt 3}{3}$
