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(** * Definition of hyperbolic functions *)
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Definition sinh (x:R) : R := (exp x - exp (- x)) / 2.
Definition tanh (x:R) : R := sinh x / cosh x.

Lemma sinh_0 : sinh 0 = 0.
Definition cos_n (n:nat) : R := (-1) ^ n / INR (fact (2 * n)).