Answer
$\frac{sin~2x}{cos~2x+1} = tan~x$
Work Step by Step
$\frac{sin~2x}{cos~2x+1} = \frac{2~sin~x~cos~x}{cos^2~x-sin^2~x+1}$
$\frac{sin~2x}{cos~2x+1} = \frac{2~sin~x~cos~x}{cos^2~x-sin^2~x+(sin^2~x+cos^2~x)}$
$\frac{sin~2x}{cos~2x+1} = \frac{2~sin~x~cos~x}{2cos^2~x}$
$\frac{sin~2x}{cos~2x+1} = \frac{sin~x}{cos~x}$
$\frac{sin~2x}{cos~2x+1} = tan~x$
