Substitute multiplication of sine and cosine for a symbolic function

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Yes, for the example I have given this would work. However, in my actual expression I have other terms, say:

eq = 2*pi*cos(th)*sin(th)*diff(omega,th,th) + cos(th) - omega*sin(th)^2

but I only want to change the term cos(th)*sin(th), so I am looking for a more general solution, which can also be applied to other functions of sines and cosines.

Then the problem is ill posed. You want some partial substitution but it's unclear how partial it should be. For example, do you want to substitute sin(th)*cos(th) (where the order of sin/cos is different) as well, do you want to substitute sin(2*th)/2 as well, or do you want to express any trigonometric function of th in terms of f? If it is just plain cos(th)*sin(th) in that fixed order and nothing in between of cos/sin, I'd convert eq to a string and perform substitution there.

I didn't think about sin(2*th)/2, so I am not worried about it now. What I want is to substitute cos(th)*sin(th) or sin(th)*cos(th), even if there is something in between, say sin(th)*diff(omega,th,th)*cos(th).

You may want to translate the problem into algebraic language by introducing a variable, say s, for sin(th) and a variable, say c, for cos(th) and then reduce the resulting polynomial in s and c modulo polynomial s*c-f.