Question

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

$\sin 45°\cos 45°$

Short answer

The exact value of$\sin 45°\cos 45°=\frac{1}{2}$

Step-by-step solution

Step 1. Given information

$\sin 45°\cos 45°$

Step 2. Solution

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