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Math Help - Hellooo/ Math problem

  1. #1
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    Exclamation Hellooo/ Math problem

    Helluuu,

    I don't really know what to say to introduce myself other than saying that i am a 19 year old, living in brazil who needs very much help!! Sorry, my english is not so good but i try for you to understand.

    The book says that i need to proof that this formula is true with all values for x:

    (5 cos x-sin x)2 = A cos 2x + B sin 2x+ C

    The book also says that A,B,C is a whole number and not decimal or fráction.
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  2. #2
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    Re: Hellooo/ Math problem

    Quote Originally Posted by MathChick View Post
    Helluuu,

    I don't really know what to say to introduce myself other than saying that i am a 19 year old, living in brazil who needs very much help!! Sorry, my english is not so good but i try for you to understand.

    The book says that i need to proof that this formula is true with all values for x:

    (5 cos x-sin x)2 = A cos 2x + B sin 2x+ C

    The book also says that A,B,C is a whole number and not decimal or fráction.
    $\sin^2(x)=\dfrac{1-\cos(2x)}{2}$

    $\cos^2(x)=\dfrac{1+\cos(2x)}{2}$

    $\sin(2x)=2\sin(x)\cos(x)$

    you should be able to complete this given those 3 identities
    Thanks from HallsofIvy
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  3. #3
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    Re: Hellooo/ Math problem

    I tried to do this:

    (5 cos x-sin x)2 = A cos 2x + B sin 2x+ C

    25 cos2 x-sin2+sin2x=

    25 cos2 x+sin2x+sin2x=

    -1+25 cos2 x+sin2x=

    24 cos2x-12+12=

    12 cos 2x+ sin 2x+ 24

    A=12
    B=1
    C=24

    I don't see what is wrong, pleaase help i honestly dont know why?
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  4. #4
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    Re: Hellooo/ Math problem

    Hello, MathChick!

    I tried to do this:

    (5 cos x-sin x)2 = A cos 2x + B sin 2x+ C

    25 cos2x - sin2x + sin2x . This is way off!

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

    . . =\;25\cos^2\!x - 10\sin x\cos x + \sin^2\!x

    . . =\;25\cos^2\!x - 5(2\sin x\cos x) + \sin^2\!x

    . . =\;25\cos^2\!x - 5\sin2x + \sin^2\!x

    . . . . . . . . . . etc. . . .

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  5. #5
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    Re: Hellooo/ Math problem

    Oh my god!! Now I understand, thank you very much!
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