The 2010 Cats won both the SEC title and the SECT championship in 2010. How common is that for the Cats?
UK won both in 1998, 2001, and 2003. Ditto in 1995. Likewise in 1986 and 1984.
The SECT was restored in 1979 so that's 7 times in 32 years.
UK joined the SEC in 1933. The SECT was dropped in 1952. UK had 20 chances to win both.
Fellow named Adolph Rupp did it (win both) 12 times in the 20 seasons.