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Math Help - Simplify expression by eliminating radical

  1. #1
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    Simplify expression by eliminating radical

    How can I simplify this expression:

    f(theta)= sqrt(1+cos(4theta))

    by eliminating the radical? Is there a specific idenity I have to use?

    Thank you, I appreciate any help!
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Maybe this can help

    \displaystyle \cos^2u = \frac{1+\cos(2u)}{2}

    \displaystyle \cos u = \sqrt{\frac{1+\cos(2u)}{2}}

    \displaystyle \sqrt{2}\cos u = \sqrt{1+\cos(2u)}

    Therefore

    \displaystyle \sqrt{2}\cos 2\theta = \sqrt{1+\cos(4\theta)}

    You still have \displaystyle \sqrt{2} in the desired expression. Is this helpful at all?
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  3. #3
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    Very helpful. Thank you!
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