Updates:
        Status: Started
        Owner: smichr

Comment #3 on issue 1368 by Vinzent.Steinberg: solve((a**2 + 1) * (sin(a*x) + cos(a*x)), x) fails
http://code.google.com/p/sympy/issues/detail?id=1368

It is zero:

In [16]: e.rewrite(exp).simplify().expand().cancel()
Out[16]: 0

But the solution can be expressed much simpler.

We really need to improve rewrite to handle sinh, cosh. And .rewrite(tan) needs to be improved:


In [18]: (sin(x)/cos(x)).rewrite(tan)
Out[18]:
       ⎛x⎞
  2⋅tan⎜─⎟
       ⎝2⎠
───────────
       2
        ⎛x⎞
1 - tan ⎜─⎟
        ⎝2⎠

(.rewrite() has a lot of potential, I have a much simpler and more powerful trigsimp() using .rewrite(exp) in the works. Currently it has to use lot's of hardcoded pattern matching due to limitations in rewrite() however.)

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