Answer
$\frac{cos~x~sin~2x}{1+cos~2x} = sin~x$
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:
$\frac{cos~x~sin~2x}{1+cos~2x}$
$=\frac{cos~x~(2~sin~x~cos~x)}{1+(2~cos^2~x-1)}$
$=\frac{2~sin~x~cos^2~x}{2~cos^2~x}$
$=sin~x$
