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Ekin = m*c^2 - m0*c^2

Where m is the relativistic mass, m0 is the rest mass and c is the speed of light.

Is it acceptable to derive E = mc^2 from this equation by saying the kinetic energy of a photon is mc^2 because it has a rest mass of zero, and thereby making a relation between photon/light energy and mass. Or is this argumentation too weak? Does the "zero rest mass" photon actually come from the derived equation?

If this derivation isn't that strong I would like to ask for another derivation which uses the relativistic momentum, relativistic kinetic energy and/or Lorentz-transformations etc. I would like to avoid: derivations that use the photon momentum from theories concerning electromagnetism, and derivations that use Taylor expansion since I havn't learned that yet. Is this possible :)?