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Perl, 47 + 1 = 48 bytes

Run with the -n flag.

say!!/^(s(in?)?|c(os?)?|t(an?)?|ln?|log?|e)+$/i

I'm not sure this regex can be golfed any further, but I'll keep trying things.

Try it online!

I downloaded a dictionary file, and the longest word I found was 11 letters -- tattletales