Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.5 Write Trigonometric Functions and Models - 14.5 Exercises - Quiz for Lessons 14.3-14.5 - Page 945: 8

$x =2 n \pi \pm \dfrac{\pi}{2}$ and $x =n \pi + (-1)^n \dfrac{\pi}{4}$

Re-arrange the given equation as: $\sqrt 2 \cos x(\sin x-\dfrac{1}{\sqrt 2})=0$ When $\sqrt 2 \cos x=0$ Therefore, the general solution of $\cos x$ is: $x =2 n \pi \pm \dfrac{\pi}{2}$ when $\sin x=\dfrac{1}{\sqrt 2}$ Therefore, the general solution of $\cos x$ is: $x =n \pi + (-1)^n \dfrac{\pi}{4}$