$\"\"$

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Prove that $\"\"$ .

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Consider $\"\"$ then $\"\"$ .

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The definition of hyperbolic trigonometry : $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Apply logirthm on each side.

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in the above equation.

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$\"\"$

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$\"\"$

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$\"\"$ .