Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 960: 23

$\dfrac{ 2 \tan \theta}{(1+\tan \theta) }$

Use the Identity $\tan 2 \theta =\dfrac{ 2 \tan \theta}{1-\tan^2 \theta}$ Thus, we have $(1-\tan \theta) \tan 2 \theta=(1-\tan \theta) \times \dfrac{ 2 \tan \theta}{1-\tan^2 \theta}$ or, $=(1-\tan \theta) \times \dfrac{ 2 \tan \theta}{(1-\tan \theta) (1+\tan \theta) }$ or, $=\dfrac{ 2 \tan \theta}{(1+\tan \theta) }$