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Math Help - How do I do this?

  1. #1
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    How do I do this?

    The question tells me to use the properties of logarithms and trigonometric idntities to verify the identity. *In this case, the brackets represent absolute value.

    ln [sec theta] = - ln [cos theta]

    Now I am not sure how to make one side equal the other.
    I am thinking:
    ln [1/cos theta]
    but I am not sure?

    Any help is appreciated.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by iluvmathbutitshard View Post
    The question tells me to use the properties of logarithms and trigonometric idntities to verify the identity. *In this case, the brackets represent absolute value.

    ln [sec theta] = - ln [cos theta]

    Now I am not sure how to make one side equal the other.
    I am thinking:
    ln [1/cos theta]
    but I am not sure?

    Any help is appreciated.
    You are on the right track, use the log-power law to change that fraction to a exponent.


    Let sec(\theta) = u

    ln(u) = -ln(u^{-1})

    Use the power law of logs log_b(a^c) = c\,log_b(a)

    ln(u) = -ln(u^{-1}) = ln([u^{-1}]^{-1}) = ln(u)

    \therefore ln(sec\theta ) = -ln \left(cos \theta \right)
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