arccosh(cosh (-15))

asked by guest
on Jan 10, 2025 at 5:08 am



You asked:

Evaluate the expression: \(\operatorname{arcosh}\left( \cosh\left( -15 \right) \right)\)

MathBot Answer:

\[\operatorname{arcosh}\left( \cosh\left( -15 \right) \right) = \log{\left(\sqrt{-1 + \cosh^{2}{\left(15 \right)}} + \cosh{\left(15 \right)} \right)} \approx 15.0\]

\[\begin{aligned}\operatorname{arcosh}\left( \cosh\left( -15 \right) \right)&=\log{\left(\cosh{\left(-15 \right)} + \sqrt{\cosh^{2}{\left(-15 \right)} - 1} \right)}\\&=\log{\left(\cosh{\left(15 \right)} + \sqrt{\cosh^{2}{\left(-15 \right)} - 1} \right)}\\&=\log{\left(\cosh{\left(15 \right)} + \sqrt{\cosh^{2}{\left(15 \right)} - 1} \right)}\\&=\log{\left(\cosh{\left(15 \right)} + \sqrt{-1 + \cosh^{2}{\left(15 \right)}} \right)}\\&=\log{\left(\sqrt{-1 + \cosh^{2}{\left(15 \right)}} + \cosh{\left(15 \right)} \right)}\end{aligned}\]

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