Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 960: 24

$-(\cos \theta+\sin \theta)$

Use the Identity $\cos 2 \theta =\cos^2 \theta-\sin^2 \theta$ Thus, we have $ \dfrac{ \cos 2 \theta}{ \sin \theta -\cos \theta}=\dfrac{\cos^2 \theta-\sin^2 \theta}{\sin \theta- \cos \theta}$ or, $= \dfrac{ (\cos \theta -\sin \theta)(\cos \theta +\sin \theta)}{\sin \theta- \cos \theta}$ or, $=-(\cos \theta+\sin \theta)$