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Math Help - How to solve for x

  1. #1
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    How to solve for x

    Hello,

    How do you solve for x? do you have to factor out cosine? how?

    -2cos(x)-2cos2(x) = 0


    Thanks!
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  2. #2
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    -2 \cos x -2 \cos(2x) = -2 \cos x - 2 (2 \cos^2x - 1) = -4 \cos^2 x - 2 \cos x + 2 (this identity comes from your other post).

    Hence
    -4 \cos^2 x - 2 \cos x + 2 = 0

    2 \cos^2 x + \cos x - 1 = 0

    Set z = \cos x, then

    2z^2 + z - 1.

    Solve for z using the quadratic formula
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  3. #3
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    Hello everyone
    Quote Originally Posted by icemanfan View Post
    ... 2z^2 + z - 1.

    Solve for z using the quadratic formula
    Or, better still, by factorising.

    Grandad

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