# Chapter 5 - Review Exercises - Page 249: 46

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

#### Work Step by Step

$\frac{cos~x~sin~2x}{1+cos~2x}$ When we graph this function, it looks like the graph of $~~sin~x$ We can verify this algebraically: $\frac{cos~x~sin~2x}{1+cos~2x}$ $=\frac{cos~x~(2~sin~x~cos~x)}{1+(2~cos^2~x-1)}$ $=\frac{2~sin~x~cos^2~x}{2~cos^2~x}$ $=sin~x$

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