The expression (or equation) eqn is considered an identity in terms of the variable x, and solve attempts to find a solution in terms of vars which satisfies the equation eqn for any value of x.

This is a one-dimensional case of a generalized pattern matching.

x should not be one of the vars.

$\mathrm{solve}\left(\mathrm{identity}\left(\sin \left(x\right)=\cos \left(ax+b\right)\,x\right)\,\left[a\,b\right]\right)$

$\left[\left[a=\mathrm{-1}\,b=\frac{\mathrm{\pi }}{2}\right]\,\left[a=1\,b=-\frac{\mathrm{\pi }}{2}\right]\right]$

$\mathrm{solve}\left(\mathrm{identity}\left(\frac{3}{x^2+4x+4}=A{\left(x+B\right)}^P\,x\right)\,\left[A\,B\,P\right]\right)$

$\left[\left[A=3\,B=2\,P=\mathrm{-2}\right]\right]$

$\mathrm{solve}\left(\mathrm{identity}\left(\frac{y}{x}=a{\left(x+c\right)}^b\,x\right)\,\left[a\,b\,c\right]\right)$

$\left[\left[a=y\,b=\mathrm{-1}\,c=0\right]\right]$