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Math Help - Proving Trigonometric Identity

  1. #1
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    Exclamation Proving Trigonometric Identity

    Hey guys can you prove this identity for me and please tell me how you do it. Since its my first time proving identites, I have no idea what to do.


    Sin theta + Sin 2 theta
    ________________________ = Tan theta

    1 + Cos theta + Cos 2 theta

    Thanks
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  2. #2
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    Quote Originally Posted by itsMoeyy View Post
    Hey guys can you prove this identity for me and please tell me how you do it. Since its my first time proving identites, I have no idea what to do.


    Sin theta + Sin 2 theta
    ________________________ = Tan theta

    1 + Cos theta + Cos 2 theta

    Thanks
    \color{blue}sin(2\theta) = 2sin(\theta)cos(\theta)

    Numerator= sin(\theta)+2sin(\theta)cos(\theta) = sin(\theta)(1+2cos(\theta))
    -------------------------------------------

    \color{blue}cos(2\theta) = cos^2(\theta)-sin^2(\theta)

    \color{blue}sin^2(\theta)+cos^2(\theta)=1

    so cos(2\theta) = 2cos^2(\theta) -1
    --------------------------------------

    Denominator ={\color{red} 1}+cos(\theta) + 2cos^2(\theta) {\color{red}-1} = cos(\theta)(1+2cos(\theta)) <br />

    Fraction now becomes

    L.H.S=\frac{sin(\theta){\color{red}(1+2cos(\theta)  )}}{cos(\theta){\color{red}(1+2cos(\theta))}}

    =\frac{sin(\theta)}{cos(\theta)}

    =tan(\theta)=R.H.S<br />

    ___________________
    things in blue are formulas
    things in red get canceled
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  3. #3
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    Where are the formula's from?
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  4. #4
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    Quote Originally Posted by itsMoeyy View Post
    Where are the formula's from?
    They are standard formulae called the double angle formulae. Look for them in your class notes or textbook.
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  5. #5
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    Ok, but how do you put the formula's into place? Like do you subtitute them into the equation. But how?
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  6. #6
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    Quote Originally Posted by itsMoeyy View Post
    Ok, but how do you put the formula's into place? Like do you subtitute them into the equation. But how?
    You substitute one expression for the other. eg. Replace \sin (2 \theta) with 2 \sin \theta \cos \theta etc.
    Last edited by mr fantastic; April 30th 2009 at 01:45 PM.
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