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Math Help - Trigonometry Identities

  1. #1
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    Trigonometry Identities

    I have an exam tomorow and I ran in to some problems with the following questions:

    1. 2sinxcos^3x - 2sin^3xcox

    and

    2. Develop a forumula for sin3x in terms of sinx

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by andymac View Post
    1. 2sinxcos^3x - 2sin^3xcox
    2sinxcos^3x - 2sin^3xcox

    Factor

    2\sin(x)\cos^{3}(x) - 2\sin^{3}(x)\cos(x)\;=\;2\sin(x)\cos(x)[\cos^{2}(x)-\sin^{2}(x)]

    Both those pieces (inside and outide the []) should look very familiar.

    2. Develop a forumula for sin3x in terms of sinx
    \sin(a+b) = \sin(a)\cos(b)\;+\;\sin(b)\cos(a)

    That's almost all you need.
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  3. #3
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    2. Develop a forumula for sin3x in terms of sinx

    Thanks in advance.
    \sin 3x=\sin (2x+x)

    \sin(a+b)=\sin a\cos b+\sin b\cos a

    And then, you will need these formulae :

    \cos 2x=1-2 \sin^2x
    \sin 2x=2 \cos x \sin x
    \cos^2x=1-\sin^2x
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