Comment #5 on issue 3204 by [email protected]: Simplifying of the sum of tan(x) and cot(x)**-1.
http://code.google.com/p/sympy/issues/detail?id=3204

This is waithing review at PR 1737 ( https://github.com/sympy/sympy/pull/1737 )

trigsimp(3*tan(x)**7 - 2/cot(x)**7, method='fu')
tan(x)**7
trigsimp(3*tan(x)**7 - 2/cot(x)**7, method='futrig')
tan(x)**7
trigsimp(3*tanh(x)**7 - 2/coth(x)**7, method='futrig')
tanh(x)**7

(Actually, with futrig you are guaranteed to always get the same hyperbolic transformations as for the trig functions because the Osborne transformation is used to replace hyperbolics with trig equivalents.)

Other than replacing all of trigsimp with a call to futrig, I don't plan to make any modifications to trigsimp.

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