Solving for a constant multiplier of a variable [duplicate]

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?

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

• @Kuba i correct it – Bendesarts Feb 12 '17 at 13:31
• Solve[r Sin[\[Alpha][t]] + l Cos[\[Phi][t]] Sin[\[Gamma][t]] == 0 /. l Cos[\[Phi][t]] -> z, z][] /. z -> l Cos[\[Phi][t]] – Bob Hanlon Feb 12 '17 at 13:40
• somewhat related: meta.mathematica.stackexchange.com/q/2078/5478 – Kuba Feb 12 '17 at 14:05

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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