[q201109300600]  次の等式を証明せよ. \begin{equation*} \begin{split} &\sinh{(-x)} = -\sinh{x}, \\ &\cosh{(-x)} = \cosh{x}, \\ &\tanh{(-x)} = -\tanh{x}. \end{split} \end{equation*}

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[q201109300700]  $\cosh^2{x} - \sinh^2{x} = 1$ を証明せよ.

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[q201109300800]  次の等式を証明せよ. \begin{equation*} \begin{split} &\tanh{x} = \frac{\sinh{x}}{\cosh{x}}, \\ &1-\tanh^2{x}=\frac{1}{\cosh^2{x}}. \end{split} \end{equation*}

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[q201109300900]  次の等式を証明せよ. \begin{equation*} \begin{split} &\sinh{(x+y)} = \sinh{x}\cosh{y}+\cosh{x}\sinh{y}, \\ &\cosh{(x+y)} = \cosh{x}\cosh{y}+\sinh{x}\sinh{y}, \\ &\tanh{(x+y)} = \frac{\tanh{x}+\tanh{y}}{1+\tanh{x}\tanh{y}}. \end{split} \end{equation*}

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[q201109301200]  $\sinh^{-1}{x} = -\log(x+\sqrt{x^2+1})$ を証明せよ.

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