Comment #2 on issue 3821 by smi...@gmail.com: trigsimp does not simplify
`cosh(z) - sinh(z)`
http://code.google.com/p/sympy/issues/detail?id=3821
trigsimp tries to work with trig functions, not exponentials.
foo.rewrite(exp) will give the desired result for all of these:
for foo in
[cos(x)+I*sin(x),cos(x)-I*sin(x),cosh(x)-sinh(x),cosh(x)+sinh(x)]:
... foo.rewrite(exp)
...
exp(I*x)
exp(-I*x)
exp(-x)
exp(x)
I'm tempted to say that this shouldn't be part of trigsimp. Perhaps part of
simplify?
from sympy.simplify.simplify import _trigs
expr
cos(I*sin(x) + cos(x)) + 2
fil = lambda x: x.is_Add and x.has(*_trigs)
act = min(x, expand_mul(x.rewrite(exp)), key=count_ops)
expr.replace(fil, act)
cos(exp(I*x)) + 2
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