Chapter 5 - Review Exercises - Page 249: 57

$tan~\theta~sin~2\theta = 2-2~cos^2~\theta$

$tan~\theta~sin~2\theta = \frac{sin~\theta}{cos~\theta}~(2~sin~\theta~cos~\theta)$ $tan~\theta~sin~2\theta = 2~sin^2~\theta$ $tan~\theta~sin~2\theta = 2~(1-cos^2~\theta)$ $tan~\theta~sin~2\theta = 2-2~cos^2~\theta$