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    $(1)cosh(arcsinh(\frac{1}{2}))$

    $cosh^{2}(arcsinh(\frac{1}{2}))=1+sinh^{2}(arcsinh (\frac{1}{2}))$

    $cosh(arcsinh(\frac{1}{2}))=\sqrt{1+(\frac{1}{2})^ {2}}=\frac{\sqrt{5}}{2}$

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    $(2) sinh(2arcsinh(\frac{1}{2}))$

    $=2sinh(arcsinh(\frac{1}{2}))cosh(arcsinh(\frac{1} {2}))$

    $=1.\frac{\sqrt{5}}{2}=\frac{\sqrt{5}}{2}$

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