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Math Help - More integration solved by use of double angle formulae

  1. #1
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    More integration solved by use of double angle formulae

    Within the same question as I previously posted about,
    there is a jump not explaining conclusions that I can't quite see how the derivation was made.

    cos cubed 2theta = (1 - sin squared 2theta)cos 2theta

    Can anyone help?

    Thanks
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  2. #2
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    Think about rewriting \cos^{3}(2\theta)=\cos^{2}(2\theta)\,\cos(2\theta), while nobody's looking.
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  3. #3
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    Oh, and by the way, I would highly recommend using parentheses around all function arguments. It makes your writing clearer.
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  4. #4
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    Quote Originally Posted by Ackbeet View Post
    Think about rewriting \cos^{3}(2\theta)=\cos^{2}(2\theta)\,\cos(2\theta), while nobody's looking.

    I have but I still can't figure out where (1 - (sin squared 2theta)) actually comes from (yes (cos squared 2theta), but how?)

    Thanks
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  5. #5
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    So, you know that \cos^{2}(\theta)+\sin^{2}(\theta)=1, I'm sure. What is \cos^{2}(x)+\sin^{2}(x)? How about \cos^{2}(y)+\sin^{2}(y)? And finally, my favorite, how about
    \cos^{2}(\text{stickfigure})+\sin^{2}(\text{stickf  igure})?

    If all those are equal to the same thing, then you can see that no matter what you put inside the parentheses, you'll get one. So you could put in, say, 2\theta.
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  6. #6
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    omg thank you so much, that is sooo easy! I've been working all day, clearly my head's given up on me. Thanks
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