Answer
$\dfrac{\sqrt 3}{2}$
Work Step by Step
We need to compute $\tan 45^{\circ} \cos 30^{\circ}$.
We use the unit circle values (where t$\tan{45^{\circ}}=1$ and $\cos{30^{\circ}}=\frac{\sqrt3}{2}$ to obtain:
$\tan 45^{\circ} \cos 30^{\circ} \\
=(1) \times (\dfrac{\sqrt 3}{2}) \\=\dfrac{\sqrt 3}{2}$