# Math Help - Half Angle Proof

1. ## Half Angle Proof

I'm having a small problem getting this problem sorted out.

LaTeX:
2\cos^2\left(\frac{\theta}{2}\right)=\left(\frac{\ sin^2\theta}{1-\cos\theta}\right)

I need to prove this equation correct. I've been able to prove all the others in my homework but I must be missing something in this one.

Any help?

2. ## Re: Half Angle Proof

Originally Posted by Bowlbase
I'm having a small problem getting this problem sorted out.

LaTeX:
2\cos^2\left(\frac{\theta}{2}\right)=\left(\frac{\ sin^2\theta}{1-\cos\theta}\right)

I need to prove this equation correct. I've been able to prove all the others in my homework but I must be missing something in this one.

Any help?

Here:

4. Half Angle Formulas

3. ## Re: Half Angle Proof

It can be useful to wright:
sin(theta)=sin(2.(theta)/2)

...

Proof from the right side to the left side:
-numerator: sin^2(a)=sin^2(2.(a/2))=1-cos^2(2.(a/2))
Use now: (a^2-b^2)=(a-b)(a+b) and then the dubble angle formula.

-denominator: 1-cos(a)=1-cos(2.(a/2))
Use the dubble angle formula.

Dubble angle formule: cos(2a)=2cos^2(a)-1

4. ## Re: Half Angle Proof

Originally Posted by Bowlbase
I'm having a small problem getting this problem sorted out.

LaTeX:
2\cos^2\left(\frac{\theta}{2}\right)=\left(\frac{\ sin^2\theta}{1-\cos\theta}\right)

I need to prove this equation correct. I've been able to prove all the others in my homework but I must be missing something in this one.

Any help?

let $t = \frac{\theta}{2}$

$2\cos^2{t} = \frac{\sin^2(2t)}{1-\cos(2t)}$

on the RHS, use the following double angle identities ...

$\sin(2t) = 2\sin{t}\cos{t}$

$\cos(2t) = 1-2\sin^2{t}$

... you'll get to the LHS in a couple of steps.

5. ## Re: Half Angle Proof

I have my method. I had the problem about 50% but was just missing one step to move me on my way. I appreciate the help everyone!

6. ## Re: Half Angle Proof

Have you solved the exercice now? Or? ...

7. ## Re: Half Angle Proof

Yeah I got it. Thanks!