Q 36. - Precalculus Enhanced with Graphing Utilities

Question

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

$\tan 45° \cos 30°$

Step-by-Step Solution

Answer

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

Step 1. Given information

$\tan 45° \cos 30°$

Step 2. Solution

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