Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 960: 25

$\cos \theta-1$

Here, $-\dfrac{\tan (\theta/2)}{\csc \theta}=-\tan (\theta/2) \sin \theta$ or $=-\dfrac{\sin (\theta/2)}{\cos \theta/2} \times [2 \sin (\theta/2) \cos (\theta/2)]$ or, $=-2 \sin^2 (\theta/2)$ or, $=-1+1 -2 \sin^2 (\theta/2)$ or, $=-1+\cos [2 (\theta/2)]$ or, $=\cos \theta-1$