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Math Help - Simplify trig expression

  1. #1
    A riddle wrapped in an enigma
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    Simplify trig expression

    Hey guys,

    I'm trying to simplify this trig expression:

    \sin 2x - \cos 3x

    I'll spare you all my attempts, but I ended up here:

    \cos x(2 \sin x - 1 + 4 \sin^2 x)

    which looks worse than what I started with.
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  2. #2
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    You could use the formula sin sin = 2cos(half the sum)*sin(half the difference), but I don't know that that looks any better:

    \sin 2x - \sin\bigl(\frac\pi2-3x\bigr) = 2\cos\bigl(\frac\pi4-\frac x2\bigr)\sin\bigl(\frac{5x}2-\frac\pi4\bigr).
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by Opalg View Post
    You could use the formula sin – sin = 2cos(half the sum)*sin(half the difference), but I don't know that that looks any better:

    \sin 2x - \sin\bigl(\frac\pi2-3x\bigr) = 2\cos\bigl(\frac\pi4-\frac x2\bigr)\sin\bigl(\frac{5x}2-\frac\pi4\bigr).
    Thanks, Opalg. Turns out it didn't do anything special. A former student of mine came to me (she thinks I'm a genius..poor girl) to help her and that was the best I could come up with.

    She came back later and told me her instructor said that all she had to do was write it without the double and triple angles. Duh! It doesn't simplify down to anything remotely simple or exotic.

    Oh well. Thanks for taking the time to look at it.


    ~Dale
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