Chapter 5 - Review Exercises - Page 249: 52

$\frac{sin~2x}{sin~x} = \frac{2}{sec~x}$

$\frac{sin~2x}{sin~x} = \frac{2~sin~x~cos~x}{sin~x}$ $\frac{sin~2x}{sin~x} = \frac{2~cos~x}{1}$ $\frac{sin~2x}{sin~x} = \frac{2}{\frac{1}{cos~x}}$ $\frac{sin~2x}{sin~x} = \frac{2}{sec~x}$