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