Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 960: 42

$x=4 n \pi$

Here, we have $ \cos \dfrac{x}{2}=1$ It has to be noted that when $\cos \dfrac{x}{2} =\cos 0$ The general solution for $\cos \theta=\cos \alpha $ is $ \theta=2 n \pi \pm \alpha$ Now, we find that the general solution for $\cos (x/2)=\cos (0)$ is $ (x/2)=2 n \pi \pm (0)$ This gives: $\dfrac{x}{2}=2 n \pi$ Hence, we have $x=4 n \pi$