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Math Help - Weird Trig Identity

  1. #1
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    Weird Trig Identity

    Establish each trig identity.

    (1) In|tan(x)| = In|sin(x)| - In|cos(x)|

    (2) In|sec(x) + tan(x)| + In|sec(x) - tan(x)| = 0

    Also: Is In the symbol for natural log?
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  2. #2
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    it's ln ... with a lower case L, no upper case I.

    I think you've seen these properties of logs on this forum before, correct?

    for (1) ... remember ln(a) - ln(b) = ln(a/b) ?

    for (2) ... remember ln(a) + ln(b) = ln(ab) ?
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  3. #3
    Super Member Matt Westwood's Avatar
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    Yes but it's not "In" it's "ln", the first character is a lowercase L not an uppercase i.
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  4. #4
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    Quote Originally Posted by magentarita View Post
    Establish each trig identity.

    (1) In|tan(x)| = In|sin(x)| - In|cos(x)|

    (2) In|sec(x) + tan(x)| + In|sec(x) - tan(x)| = 0

    Also: Is In the symbol for natural log?
    Why didn't you apply what you learned from logarithms in this forum here?

    1.  \tan{x} = \frac{\sin{x}}{\cos{x}}

    \ln{\tan{x}} = \ln{\frac{\sin{x}}{\cos{x}}} = \ln{\sin{x}} - \ln{\cos{x}}

    2. \ln{(\sec{x} + \tan{x})} + \ln{(\sec{x} - \tan{x})}

    \ln{[(\sec{x} + \tan{x})(\sec{x} - \tan{x})]}

    \ln{(\sec^2{x} - \tan^2{x})}

    You should know that 1 + \tan^2{x} = \sec^2{x}

    Thus:
    \ln{1} = 0
    Last edited by Chop Suey; August 24th 2008 at 03:47 PM.
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  5. #5
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    Thanks...

    I thank you all, especially Chop Suey.
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