The question is simple as that. I have:

$Assumptions[v \[Element] Reals]
x[u_, v_] := {f[u], g[u] Cos[v], g[u] Sin[v]}
pil[{x_, y_, z_}, {a_, b_, c_}] := x*a + y*b - z*c
pil[D[x[u, v], u], D[x[u, v], v]]
-2 Cos[v] g[u] Sin[v] Derivative[1][g][u]

and for some reason, Simplify won't turn the last expression into -Sin[2v] Derivative[1][g][u]. I looked a bit around before asking, so I also tried FullSimplify and $Assumptions[v \[Element] Reals], to no avail. Why is all of this going wrong? Can someone explain to me, please? (I find a bit hard to trust a program that can't use the simple fact that $\sin(2v) = 2 \sin v \cos v$.)

  • 2
    $\begingroup$ Try using TrigReduce $\endgroup$ – RunnyKine Oct 12 '14 at 22:19
  • $\begingroup$ It worked. Thank you very much! Anyway, I'll leave the question here, in case someone shows up to give a more technical explanation for the problem. $\endgroup$ – Ivo Terek Oct 12 '14 at 22:21
  • 1
    $\begingroup$ The reason is Mathematica is such a large system with a lot of rewrite rules and special cases of those rules. So sometimes you'll have to use available special functions to force it to do certain simplifications as in this case. $\endgroup$ – RunnyKine Oct 12 '14 at 22:26
  • $\begingroup$ That makes it clearer! $\endgroup$ – Ivo Terek Oct 12 '14 at 22:28

You can use TrigReduce to do what you want:

TrigReduce[-2 Cos[v] g[u] Sin[v] Derivative[1][g][u]]
-g[u] Sin[2 v] Derivative[1][g][u]
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