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Math Help - Solving Identities

  1. #1
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    Solving Identities

    4sin^2 = cos x + 3
    4(1-cos^2) = cos + 3
    -4cos^2 -cos x +1
    4cos^2 + cos x - 1

    I was thinking of using quadratic formula as I tried to factor

    Product -4
    Sum 1

    or

    cos x (4 cos x + 1) -1 *I don't know what to do since it is = to -cos x / cos x
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quan View Post
    4sin^2 = cos x + 3
    4(1-cos^2) = cos + 3
    -4cos^2 -cos x +1
    4cos^2 + cos x - 1

    I was thinking of using quadratic formula as I tried to factor

    Product -4
    Sum 1

    or

    cos x (4 cos x + 1) -1 *I don't know what to do since it is = to -cos x / cos x
    This is not an identity, it is an equation. And you didn't even consistently put in the argument of the functions! "cos " is meaningless in this situation without the argument.

    4sin^2(x) = cos(x) + 3

    Now, sin^2(x) + cos^2(x) = 1, so we have
    4(1 - cos^2(x)) = cos(x) + 3

    4 - 4cos^2(x) = cos(x) + 3

    4cos^2(x) + cos(x) - 1 = 0

    Now let y = cos(x):
    4y^2 + y - 1 = 0

    The quadratic formula says that
    y = \frac{-1 \pm \sqrt{17}}{8}

    Thus
    cos(x) = \frac{-1 \pm \sqrt{17}}{8}

    So
    x = cos^{-1} \left ( \frac{-1 \pm \sqrt{17}}{8} \right )

    You can do both of them on your calculator. I leave the rest to you.

    -Dan
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