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Math Help - Equation with cos

  1. #1
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    Equation with cos

    Solve the equation: 2\cos{5x}+2\cos{4x}+2\cos{3x}+2\cos{2x}+2\cos{x}+1  =0
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  2. #2
    Junior Member qspeechc's Avatar
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    cos(ax) = cos((a-1)x + x)
    expand and continue in that fashion
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  3. #3
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    Quote Originally Posted by qspeechc View Post
    cos(ax) = cos((a-1)x + x)
    expand and continue in that fashion
    Could you explain it please. I just couldn't solve the for x using only the \cos(ax) = \cos((a-1)x + x). Thx
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  4. #4
    Junior Member qspeechc's Avatar
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    So you have:

    2cos5x + 2cos4x + 2cos3x + 2cos2x + 2cosx + 1 = 0

    And I said:
    cos(ax) = cos((a-1)x + x)
    expand and continue in that fashion

    So, for instance, lets look at the case where a = 5:

    cos5x = cos(4x + x)

    Now that is of the form cos(A+B), which we know how to expand:
    cos(A+B) = cosA.cosB - sinA.sinB

    So, for cos5x:
    cos5x = cos(4x + x)
    . = cos(4x).cos(x) - sin(4x).sin(x)

    And then you can do the same sort of expansions with sin(4x), cos(4x), cos(3x) etc., until you are satisfied you have simplified it enough to solve.
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