Here's the question you clicked on:
AonZ
Eliminate A from each pair of parametric equations x = 2tan( A/2) y = cosA
$$\large{ 2 tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-cos(a)}{sin(a)}}\\ \color{red}{y} = \color{blue}{cos(a)} \ \ \ thus\\ 2tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-y}{sin(a)}} \implies \pmatrix{\frac{2-2y}{sin(a)}}\\ x=\frac{2-2y}{sin(a)} \implies \color{blue}{sin(a)} = \color{red}{\frac{2-2y}{x}} } $$
then just use the identity of \(\large sin^2+cos^2 =1\) to get your equation
how does \[{ 2 \tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-\cos(a)}{\sin(a)}}\\ }\]
http://www.freemathhelp.com/images/halfangles.png half-angle identities, check your textbook formulas, or a formula cheatsheet you may have
the picture there shows 2 for tangent, there are 3, at least on my sheet :)