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

1. jdoe0001

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

2. jdoe0001

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

3. AonZ

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

4. jdoe0001

http://www.freemathhelp.com/images/halfangles.png half-angle identities, check your textbook formulas, or a formula cheatsheet you may have

5. jdoe0001

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

6. AonZ

ok thanks i got it :)