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Math Help - Half Angle Proof

  1. #1
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    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)

    Half Angle Proof-eqn8136.png

    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?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Half Angle Proof

    Quote Originally Posted by Bowlbase View Post
    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)

    Click image for larger version. 

Name:	eqn8136.png 
Views:	52 
Size:	1.7 KB 
ID:	21862

    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
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  3. #3
    MHF Contributor Siron's Avatar
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    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
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  4. #4
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    Re: Half Angle Proof

    Quote Originally Posted by Bowlbase View Post
    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)

    Click image for larger version. 

Name:	eqn8136.png 
Views:	52 
Size:	1.7 KB 
ID:	21862

    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.
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  5. #5
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    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!
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Half Angle Proof

    Have you solved the exercice now? Or? ...
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  7. #7
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    Re: Half Angle Proof

    Yeah I got it. Thanks!
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