A Ge pixel array detector with 100 segments was applied to fluorescence X-ray absorption spectroscopy, probing the local structure of high-temperature superconducting thin-film single crystals (100 nm in thickness). Independent monitoring of pixel signals allows real-time inspection of artifacts owing to substrate diffractions. By optimizing the grazing-incidence angle theta and adjusting the azimuthal angle phi, smooth extended X-ray absorption fine structure (EXAFS) oscillations were obtained for strained (La,Sr)2CuO4 thin-film single crystals grown by molecular beam epitaxy. The results of EXAFS data analysis show that the local structure (CuO6 octahedron) in (La,Sr)2CuO4 thin films grown on LaSrAlO4 and SrTiO3 substrates is uniaxially distorted changing the tetragonality by approximately 5 x 10(-3) in accordance with the crystallographic lattice mismatch. It is demonstrated that the local structure of thin-film single crystals can be probed with high accuracy at low temperature without interference from substrates.