Question

Find the exact value of each expression. Do not use a calculator.

$\tan 45°\cos 30°$

Short answer

The exact value of$\tan 45°\cos 30°=\frac{\sqrt{3}}{2}$

Step-by-step solution

Step 1. Given information

$\tan 45°\cos 30°$

Step 2. Solution

$$\begin{gathered} \tan 45°=1 \\ \cos 30°=\frac{\sqrt{3}}{2} \\ \mathrm{Putting}\mathrm{the}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{expression}\mathrm{we}\mathrm{get}, \\ 1\times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2} \\ \mathrm{So}, \\ \tan 45°\cos 30°=\frac{\sqrt{3}}{2} \end{gathered}$$