Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 960: 39

$x=\dfrac{\pi}{4}, \dfrac{7 \pi}{4}$

Use the Half angle formula: $ \dfrac{1-\cos x}{\sin x}=\dfrac{2 -\sqrt 2}{2 \sin x}$ or, $(1-\cos x) \times (2\sin x) =(\sin x) \times (2-\sqrt 2)$ $\implies 2 (1-\cos x)=(2-\sqrt 2)$ Here, $2-2 \cos x =2-\sqrt 2$ or, $ \cos x= \dfrac{\sqrt 2}{2}$ Thus, we have $x=\dfrac{\pi}{4}, \dfrac{7 \pi}{4}$