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Math Help - how cosh(ln(4+sqr(17)) becomes asqrt(17)

  1. #1
    Junior Member
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    how cosh(ln(4+sqr(17)) becomes asqrt(17)

    Hi, at a point Q, x = (4+sqrt(17)

    find the y co-ordinate, expressing your answer in surd form

    x can also be written arsinh(4)

    but I don't know if that helps.

    I'm stumped :\
    Thanks
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  2. #2
    Senior Member Sampras's Avatar
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     \text{cosh} \ x = \frac{e^{x}+e^{-x}}{2} . And  \text{sinh}^{-1} \ x = \log(x+ \sqrt{x^2+1}) .
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  3. #3
    MHF Contributor
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    Hi

    \cosh(\ln(4+\sqrt{17})) = \frac{e^{\ln(4+\sqrt{17})}+e^{-\ln(4+\sqrt{17})}}{2}

    \cosh(\ln(4+\sqrt{17})) = \frac{4+\sqrt{17}+\frac{1}{4+\sqrt{17}}}{2}

    \cosh(\ln(4+\sqrt{17})) = \frac{17+4\sqrt{17}}{4+\sqrt{17}}

    \cosh(\ln(4+\sqrt{17})) = \frac{17+4\sqrt{17}}{4+\sqrt{17}}\:\frac{\sqrt{17}-4}{\sqrt{17}-4}

    \cosh(\ln(4+\sqrt{17})) = (17+4\sqrt{17})(\sqrt{17}-4) = \sqrt{17}
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  4. #4
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    thank you both very much. it's easy peasy
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