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cosh^2 x - sinh^2 x = 1

((e^x + e^-x)/ 2)^2 - ((e^x - e^-x)/ 2)^2 = 1

1/4 (e^2x + 2e^xe^-x + e^-2x) - 1/4 (e^2x + 2e^xe^-x + e^-2x) = 1

1/4 e^2x + 1/4 (2) + 1/4 e^-2x - 1/4 e^2x + 1/4 (2) - 1/4 e^-2x = 1

1/2 + 1/2 = 1

1 = 1

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