Comment #4 on issue 1368 by asmeurer: solve((a**2 + 1) * (sin(a*x) + cos(a*x)), x) fails
http://code.google.com/p/sympy/issues/detail?id=1368
I have a much simpler and more powerful trigsimp() using .rewrite(exp) in the works
I look forward to seeing that! There's also the approach by Fu, et. al., which has been floating around here for some time. Whenever I get around to implementing tangent integration in risch_integrate() (issue 2010), I am going to need strong trig simplification, because the only way to integrate functions with sin and cos is to apply the transformation you noted above (i.e., it can only integrate tangents), after which you are going to want to convert back to sines and cosines, which is fine, because you can use tan(x/2) == (1 - cos(x))/sin(x) == sin(x)/(1 + cos(x)), but you then need to simplify the nastiness that will result from tan(x)**n terms.
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