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Mathematica

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  • $\begingroup$ Try Tan -> (Sin[#]/Cos[#] &). $\endgroup$ Commented Dec 13, 2015 at 5:09
  • $\begingroup$ I don't know if this is what you're looking for, but (1 - Tan[x])/(Sin[x] - Cos[x]) // Simplify gives -Sec[x]. $\endgroup$ Commented Dec 13, 2015 at 5:11
  • $\begingroup$ @Rahul I am looking at how to apply pencil and paper type steps to simplify the expression. I am aware of the //Simplify expression. $\endgroup$ Commented Dec 13, 2015 at 5:13
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    $\begingroup$ Your replacement is working, I think. The problem is that Mathematica automatically simplifies Sin[x]/Cos[x] to Tan[x]. If you're going to do step-by-step math, perhaps consider using undefined symbols like sin[x] and cos[x]. $\endgroup$ Commented Dec 13, 2015 at 5:18
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    $\begingroup$ Ah, I forgot the auto-simplification! (@march, that's the answer I believe.) You'll probably want to use Activate[]/Inactivate[] here. $\endgroup$ Commented Dec 13, 2015 at 5:21