## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$\dfrac{\sqrt 3}{2}$
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: $\tan 45^{\circ} \cos 30^{\circ} \\ =(1) \times (\dfrac{\sqrt 3}{2}) \\=\dfrac{\sqrt 3}{2}$