Solving for a constant multiplier of a variable

Question

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?

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]] — Bob Hanlon, Feb 12 '17 at 13:40
somewhat related: http://meta.mathematica.stackexchange.com/q/2078/5478 — Kuba, Feb 12 '17 at 14:05

score 1 · Answer 1 · answered Feb 12 '17 at 15:04

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

0

1 Answers1