Pinning down the kaon form factors in K+ -> mu+ nuₘu gamma decay

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We find that the normal muon polarization in the decay K->mu nuₘu gamma is very sensitive to the values of the kaon vector Fᵥ and axial-vector Fₐ form factors. It is shown that the ongoing KEK-E246 experiment can definitely determine the signs of the sum of the form factors if their difference is fixed from other considerations. This method can also verify the form factor values and signs obtained from the K+ -> l+ nuₗ e+ e- decays. A new experiment with sensitivity to the normal and transverse muon polarizations of about 10-4 will provide a unique possibility to determine the Fᵥ and Fₐ values with a few percent accuracy.