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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 simpl_cos_n :
forall n:nat, cos_n (S n) / cos_n n = - / INR (2 * S n * (2 * n + 1)).