Chapter 8.4, Problem 5QR

To determine

To calculate: simplify the function.

Answer to Problem 5QR

Function $\sqrt{1+\cos 2x}=\sqrt{2}\cos x$ .

Explanation of Solution

Given information: Function $\sqrt{1+\cos 2x}\text{ on }\left[0,\frac{\pi }{2}\right]$ .

Calculation:

Function $\sqrt{1+\cos 2x}\text{ on }\left[0,\frac{\pi }{2}\right]$

  $\begin{array}{l}\because \cos 2x=2{\cos }^{2}x-1\\ \sqrt{1+\cos 2x}=\sqrt{1+2{\cos }^{2}x-1}\\ \sqrt{1+\cos 2x}=\sqrt{2{\cos }^{2}x}\\ \sqrt{1+\cos 2x}=\sqrt{2}\cos x\end{array}$