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expand hyperbolic trig functions

asked 2014-07-23 08:48:08 -0600

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.

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answered 2014-07-23 09:24:57 -0600

FrédéricC gravatar image

updated 2014-07-23 09:32:20 -0600

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
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Comments

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

rws gravatar imagerws ( 2014-07-23 10:01:53 -0600 )edit

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

kcrisman gravatar imagekcrisman ( 2014-07-23 10:14:14 -0600 )edit

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Asked: 2014-07-23 08:48:08 -0600

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Last updated: Jul 23 '14