Comment #9 on issue 1562 by asmeurer: Have trigsimp apply factor and
Poly.cancel() to sin's and cos's
http://code.google.com/p/sympy/issues/detail?id=1562
OK, here is an example of where polynomial manipulation is not enough to
trigsimplify. We need to replace
sin**2 with 1 - cos**2 or visa-versa to simplify these kinds of expressions:
This is in Mateusz's new ploys branch:
# There is nothing wrong with factor, it's just that algebraically (i.e.,
not taking trig identities into account), this
expression is not factorable.
In [14]: factor(-2*cos(x)**2 + cos(x)**4 - sin(x)**4)
Out[14]:
2 4 4
- 2⋅cos (x) + cos (x) - sin (x)
# But this works fine
In [15]: (-2*cos(x)**2 + cos(x)**4 - sin(x)**4).subs(cos(x)**2, 1 -
sin(x)**2)
Out[15]:
2
⎛ 2 ⎞ 2 4
-2 + ⎝1 - sin (x)⎠ + 2⋅sin (x) - sin (x)
# for more complex expressions, we should probably somehow only expand that
parts that have been changed
In [16]: expand((-2*cos(x)**2 + cos(x)**4 - sin(x)**4).subs(cos(x)**2, 1 -
sin(x)**2))
Out[16]: -1
# Oh, and by the way, trigsimp cannot do it.
In [17]: trigsimp(-2*cos(x)**2 + cos(x)**4 - sin(x)**4)
Out[17]:
2 4 4
- 2⋅cos (x) + cos (x) - sin (x)
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