Hyperbolic identities
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Hyperbolic Identities
Like the circle functions, there are many relationships that hold between hyperbolic functions. First formula cosh (squared) x - sinh (squared) x = 1 [Equation goes here - download the original to see it.] Second formula 1 - tanh (squared) x = sech (squared) x [Equation goes here - download the original to see it.] Third formula From the graphs of sinh x, cosh x and tanh x we can deduce cosh(-x) = coshx. sinh (-x) = sinh x. tanh(-x) = tanh x [Equation goes here - download the original to see it.] cosh(-x) = cosh x [Equation goes here - download the original to see it.] [Diagram goes here - download the original to see it.] sinh (-x) = -sinh x [Equation goes here - download the original to see it.] [Diagram goes here - download the original to see it.] tanh(-x) = -tanh x [Equation goes here - download the original to see it.] [Diagram goes here - download the original to see it.] Fourth formula: We have already shown that [Equation goes here - download the original to see it.] Fifth formula: sinh2x = 2sinhx.coshx. Proof Equation goes here - download the original to see it.] Sixth formula cosh 2x = cosh(squared)x + [Equation goes here - download the original to see it.]
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Hyperbolic identities
1 Hyperbolic Identities
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