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Math Help - Cosine, sine subtraction problem

  1. #1
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    Cosine, sine subtraction problem

    This is actually part of a calculus problem, but the part I was struggling with was pure trig, so here you are:
    2cos^2(2x) - 2sin^2(2x)

    The back of the book simplifies this to:
    2cos(4x)
    How?
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by seuzy13 View Post
    This is actually part of a calculus problem, but the part I was struggling with was pure trig, so here you are:
    2cos^2(2x) - 2sin^2(2x)

    The back of the book simplifies this to:
    2cos(4x)
    How?
    you should know that

    \cos 2x =\cos ^2 x - \sin ^2 x ok so


    2\cos ^2 (2x) - 2\sin ^2(2x)

    2( \cos ^2 (2x) - \sin ^2 (2x) )

    2( \cos 2(2x)) = 2\cos (4x)
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  3. #3
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    Quote Originally Posted by Amer View Post
    you should know that

    \cos 2x =\cos ^2 x - \sin ^2 x ok so


    2\cos ^2 (2x) - 2\sin ^2(2x)

    2( \cos ^2 (2x) - \sin ^2 (2x) )

    2( \cos 2(2x)) = 2\cos (4x)
    \cos 2x =\cos ^2 x - \sin ^2 x
    Do you happen to know what the general term for this kind of equation is, so I can look it up in my trig book? The problem is when I went to calculus, I skipped trig, so some of these basic "you should know" things are completely new to me.
    Also confused about how you did the last line:
    2( \cos 2(2x)) = 2\cos (4x)
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  4. #4
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by seuzy13 View Post
    \cos 2x =\cos ^2 x - \sin ^2 x
    Do you happen to know what the general term for this kind of equation is, so I can look it up in my trig book? The problem is when I went to calculus, I skipped trig, so some of these basic "you should know" things are completely new to me.
    Also confused about how you did the last line:
    2( \cos 2(2x)) = 2\cos (4x)
    there is no general term you should memories formulas

    memories the formula in this link not all but the important ones like

    \sin 2x =?? , \cos 2x = ?? , sin^2 x + cos^2 x =??

    something like that

    Math Forum: Ask Dr. Math FAQ: Trigonometry Formulas

    the thing that you are confused from it , I just multiply 2(2x) = 4x what hard in this .
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  5. #5
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    Quote Originally Posted by Amer View Post
    there is no general term you should memories formulas

    memories the formula in this link not all but the important ones like

    \sin 2x =?? , \cos 2x = ?? , sin^2 x + cos^2 x =??

    something like that

    Math Forum: Ask Dr. Math FAQ: Trigonometry Formulas

    the thing that you are confused from it , I just multiply 2(2x) = 4x what hard in this .
    Confused about why you are multiplying 2(2x) I guess. How you got from second to last step to the last step. Nothing hard about the actual multiplication. Haha.
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  6. #6
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    Never mind. I think I get it now. Thanks a bunch!
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