Thread: 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?

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

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

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



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





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

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!

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

Yeah I got it. Thanks!