When I ask Mathematica to do this:
(Sin[2 x] - Tan[2 x])/x^3 /. Tan[x_] -> Sin[x]/Cos[x] It makes no change because Mathematica interprets Tan[x] as the same thing as Sin[x]/Cos[x]. Is it possible to force Mathematica to rewrite:
$$\frac{\sin(2x)-\tan(2x)}{x^3}$$
As:
$$\frac{\sin(2x)-\frac{\sin(x)}{\cos(x)}}{x^3}?$$
I know this has to do with evaluation control but I'm looking at the documentation and am not finding anything that resembles this. At the time, I know I could make this converting everything to string and using string substitutions but I guess this would be kinda cumbersome for my needs.
(Sin[2 x] - Tan[2 x])/x^3 /. Tan[x_] -> HoldForm[Sin[x]/Cos[x]]? $\endgroup$