Electromagnetically induced transparency (EIT) cooling uses quantum interference to suppress carrier scattering and enhance red-sideband transitions, providing a route to reducing the motional energy of trapped atoms. We theoretically and experimentally investigate EIT spectroscopy and cooling of a single ^133Cs atom confined in a 1064 nm optical dipole trap. A driven \Lambda system is formed by the ground states |6S_1/2,F=4,m_F=4\rangle and |6S_1/2,F=3,m_F=3\rangle and the excited state |6P_1/2,F'=4,m_F'=4\rangle. A dressed-state analysis and a Lindblad master equation describe the dark resonance, the nearby bright-state resonance, and the ideal sideband-cooling limit. Experimentally, we characterize the EIT spectrum through the time dependence of a state-selective retention signal associated with the initial state |6S_1/2,F=4,m_F=4\rangle, using microwave state mapping followed by push-out detection. At each two-photon detuning, a two-parameter exponential fit yields an effective net decay rate. Weighted fitting in the lifetime domain, using a scaled ideal steady-state excitation spectrum and a background decay term, reveals an asymmetric Fano profile with suppressed decay near the dark resonance. This observable includes the effects of internal-state population transfer and trap loss and therefore does not directly measure the absolute photon-scattering rate. Spectroscopy and cooling employ different optical parameters. For cooling, the coupling detuning is \Delta_c/2\pi=42.5 MHz, and the coupling and probe Rabi frequencies are \Omega_c/2\pi=2.85 MHz and \Omega_p/2\pi=0.30 MHz, respectively. The calculated bright-state shift is approximately 48.3 kHz, close to the measured radial trap frequency of 52 kHz, favoring red-sideband cooling. After 10 ms of EIT cooling, binomial maximum-likelihood fits of the raw release--recapture counts using the same Monte Carlo model yield a temperature reduction from (17.55±0.84) \mu\mathrm K after polarization-gradient cooling to (8.98±0.44) \mu\mathrm K. The uncertainties are statistical standard errors (1\sigma) for fixed trap parameters. Assuming a thermal distribution of the radial motion, the corresponding mean phonon number decreases from approximately 6.55 to 3.12. These measurements demonstrate a reduction in motional energy after a finite cooling time; they do not establish the steady-state cooling limit or ground-state preparation. The results show how state-selective retention measurements can resolve single-atom EIT resonances and provide an experimental reference for selecting EIT-cooling parameters in optical tweezers.