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This question already has an answer here:

I would like to make this manipulation:

Solve[r Sin[α[t]] + l Cos[ϕ[t]] Sin[γ[t]] == 0, l*Cos[ϕ[t]]]

But it seems that the Solve function works only with variables.

However,

Solve[r Sin[α[t]] + l Cos[ϕ[t]] Sin[γ[t]] == 0, Cos[ϕ[t]]] 

works

Have you an idea to have a direct way to code the first code line?

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marked as duplicate by Feyre, MarcoB, Young, happy fish, ciao Feb 13 '17 at 10:41

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ @Kuba i correct it $\endgroup$ – Bendesarts Feb 12 '17 at 13:31
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    $\begingroup$ Solve[r Sin[\[Alpha][t]] + l Cos[\[Phi][t]] Sin[\[Gamma][t]] == 0 /. l Cos[\[Phi][t]] -> z, z][[1]] /. z -> l Cos[\[Phi][t]] $\endgroup$ – Bob Hanlon Feb 12 '17 at 13:40
  • $\begingroup$ somewhat related: meta.mathematica.stackexchange.com/q/2078/5478 $\endgroup$ – Kuba Feb 12 '17 at 14:05
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I have a simple mind, so I tried the obvious.

sol =
 Map[
   Times[l, #] &,
   Solve[r Sin[α[t]] + l Cos[ϕ[t]] Sin[γ[t]] == 0, 
    Cos[ϕ[t]]],
   {3}][[1, 1]]

l Cos[ϕ[t]] -> -r Csc[γ[t]] Sin[α[t]]

Check

r Sin[α[t]] + l Cos[ϕ[t]] Sin[γ[t]] /. sol

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