hyperbolic-identities-and-equations

Hyperbolic identities & equations

Are there identities linking the hyperbolic functions to the circular trig functions?

• Yes – these can be seen using de Moivre’s Theorem to write

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• Compare these with the definitions for the hyperbolic functions

  • <img alt=”cosh x equals 1 half open parentheses straight e to the power of x plus straight e to the power of negative x end exponent close parentheses” data-mathml='<math ><semantics><mrow><mi>cosh</mi><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><msup><mi mathvariant=”normal”>e</mi><mi>x</mi></msup><mo>+</mo><msup><mi mathvariant=”normal”>e</mi><mrow><mo>-</mo><mi>x</mi></mrow></msup></mrow></mfenced></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”47″ role=”math” 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