Question

Eliminate A from each pair of parametric equations
x = 2tan( A/2)
y = cosA

Answer 1

$$\large{
2 tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-cos(a)}{sin(a)}}\\
\color{red}{y} = \color{blue}{cos(a)} \ \ \ thus\\
2tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-y}{sin(a)}} \implies \pmatrix{\frac{2-2y}{sin(a)}}\\
x=\frac{2-2y}{sin(a)} \implies \color{blue}{sin(a)} = \color{red}{\frac{2-2y}{x}}
}
$$

Answer 2

then just use the identity of \(\large sin^2+cos^2 =1\) to get your equation

Answer 3

how does
\[{ 2 \tan\pmatrix{\frac{a}{2}}=2\pmatrix{\frac{1-\cos(a)}{\sin(a)}}\\ }\]

Answer 4

http://www.freemathhelp.com/images/halfangles.png

half-angle identities, check your textbook formulas, or a formula cheatsheet you may have

Answer 5

the picture there shows 2 for tangent, there are 3, at least on my sheet :)

Answer 6

ok thanks i got it :)