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