We uncover hidden spectral symmetries of the Teukolsky equation in Kerr(-de Sitter) black holes, recently conjectured by Aminov, Grassi and Hatsuda (arXiv: 2006.06111 arXiv: 2007.07906, 2020) zero cosmological constant case. Using these symmetries, we provide a new, simpler proof mode stability for subextremal Kerr holes. also present partial result Kerr-de Sitter