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Math Help - sum to product formula

  1. #1
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    sum to product formula

    use sum to product formula:

    [sinx+siny=2sin(x+y)cos(x-y)] to solve [0,2pi).

    sin3x + sinx = 0

    -----------------------

    this is what i did and got stuck on:

    1. sin(3x+x)
    2. (2sin(3x+x)/2)cos(3x-x)/2
    3. 2sin(4x/2)cos(2x/2)
    4. 2sin2xcosx

    stuck there, what do i do next?
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  2. #2
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    Quote Originally Posted by algebra2 View Post
    use sum to product formula:

    [sinx+siny=2sin(x+y)cos(x-y)] to solve [0,2pi).

    sin3x + sinx = 0
    Sorry, nothing of what you did was correct.

    sin(3x) = sin(2x + x) = sin(2x)~cos(x) + sin(x)~cos(2x)

    = 2~sin(x)~cos^2(x) + sin(x)(1 - 2sin^2(x))

    = 2~sin(x)(1 - sin^2(x)) + sin(x)(1 - 2sin^2(x))

    = 4~sin^3(x) + 3~sin(x)

    So solve
    4~sin^3(x) + 3~sin(x) + sin(x) = 0

    4~sin^3(x) + 4~sin(x) = 0

    -Dan
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