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Math Help - [SOLVED] double angle

  1. #1
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    [SOLVED] double angle

    simplify

    cos2xcosx+sin2xsinx

    a cosx
    b sinx
    c cos3x
    d sin3x


    what I tried was....
    <br />
(1-2sin^2x)cosx+2sinxcosx
    cosx-2sin^2xcosx+2sinxcosx ?
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  2. #2
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    Use \cos 2x=2\cos^2x-1, \sin 2x=2\cos x \sin x and \sin^2 x = 1-\cos^2 x

    \cos x(2\cos^2x-1)+2\cos x \sin^2 x=\cos x(2\cos^2 x-1 + 2(1-\cos^2 x))=\cos x
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  3. #3
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    Quote Originally Posted by brentwoodbc and edited by Mr F View Post
    simplify

    cos(2x) cos(x) + sin(2x) sin(x)

    a cosx
    b sinx
    c cos3x
    d sin3x


    what I tried was....
    (1- 2 \sin^2 x) \cos x + 2 \sin x \cos x Mr F says: *Ahem* Haven't you forgotten the red sin(x) from above .....? Put it in and expand:

    \cos x - 2 \sin^2 x \cos x + 2 \sin {\color{red}^2} x \cos x ?
    ..
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  4. #4
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    Thank you.
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