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  "body": "\n## Statement\n\nFor all real numbers $x$ and $y$,\n$$\\sinh(x + y) = \\sinh x \\cosh y + \\cosh x \\sinh y,$$\n$$\\cosh(x + y) = \\cosh x \\cosh y + \\sinh x \\sinh y.$$\n\n## Remarks\n\nExpand the right sides with the definitions and use [[$e^{x+y} = e^x e^y$|0E8HNVBCSP]].\nWith $y = x$, they give $\\sinh 2x = 2 \\sinh x \\cosh x$ and $\\cosh 2x = \\cosh^2 x + \\sinh^2 x$.\nMathlib states the first formula as `Real.sinh_add`.\n\n## Explanations\n\n### L1 human\n\nThese formulas look like the trigonometric addition formulas.\nThe only change is the plus sign in the formula for $\\cosh$.\n",
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