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Math Help - Triangle Problem

  1. #1
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    Triangle Problem

    Hey sorry I'm having a bit of mind blank today, can anyone give me a hint to get me started with this
    If A, B and C are the angles of a triangle prove that
    <br />
\cos \begin{pmatrix} \frac{B-C}{2} \end{pmatrix} - \sin \begin{pmatrix} \frac{A}{2} \end{pmatrix} = 2 \sin \begin{pmatrix} \frac{B}{2} \end{pmatrix} \sin \begin{pmatrix} \frac{C}{2} \end{pmatrix}<br />
    Cheers

    Simon
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by thelostchild View Post
    Hey sorry I'm having a bit of mind blank today, can anyone give me a hint to get me started with this

    Cheers

    Simon
    Observe that A = \pi - B - C(Why?), so

    \sin \left(\frac{A}2\right) = \sin \left(\frac{\pi - B - C}2\right) = \sin \left(\frac{\pi}2  - \frac{B + C}{2}\right) = \cos \left(\frac{B + C}{2}\right)

    Can you continue now?
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  3. #3
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    thank you, I'm feeling pretty stupid now I kept looking for how I could do it geometrically that is much easier
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