expand hyperbolic trig functions

Part of a symbolic expression is

ex = 2*e^(1/2*x)*sinh(1/2*x)

How to substitute sinh(x) with its expansion (e^x-e^(-x))/2 and simplify ex to e^x-1? I have tried all expand and simplify functions.

1 Answer

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Is this what you need ?

sage: ex2 = ex.subs_expr(sinh(x/2) == (exp(x/2)-exp(-x/2))/2)
sage: ex2.exp_simplify()
e^x - 1

or even better

sage: w0 = SR.wild(0)
sage: ex2 = ex.subs_expr(sinh(w0) == (exp(w0)-exp(-w0))/2)
sage: ex2.exp_simplify()
e^x - 1

This substitution should happen on expand() or expand_trig() IMHO.

rws ( 2014-07-23 17:01:53 +0100 )edit

Perhaps, but I'm not sure if it is available in any of the expansions in Ginac or Maxima.

kcrisman ( 2014-07-23 17:14:14 +0100 )edit

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Asked: 2014-07-23 15:48:08 +0100

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Last updated: Jul 23 '14