  Muon component of extensive air showers (EAS) initiated by cosmic ray
particles carries information on the primary particle identity. We show that
the muon content of EAS could be measured in a broad energy range from 10-100
TeV up to ultra-high-energy cosmic ray range using wide field-of-view imaging
atmospheric Cherenkov telescopes observing strongly inclined or nearly
horizontal EAS from the ground of from high altitude. Cherenkov emission from
muons in such EAS forms a distinct component (halo or tail) of the EAS image in
the telescope camera. We show that detection of the muon signal could be used
to measure composition of the cosmic ray spectrum in the energy ranges of the
knee, the ankle and of the Galactic-to-extragalactic transition. It could also
be used to veto the cosmic ray background in gamma-ray observations. This
technique provides a possibility for up to two orders of magnitude improvement
of sensitivity for gamma-ray flux in the energy band above 10 PeV, compared to
KASCADE-Grande, and an order-of-magnitude improvement of sensitivity in the
multi-EeV energy band, compared to Pierre Auger Observatory.
