The 30-year-old actress is yet to confirm her romance with Cook but has continued to throw hints about her new relationship, reported Ace Showbiz.
"That's what happy looks like," she wrote and added a love emoji besides the picture.
Cuoco was previously married to former professional tennis player Ryan Sweeting, 28. The couple tied the knot in December 2013 after roughly six months of dating. They mutually decided to part ways two years later in December 2015.
She prompted romance rumours with Cook after he started showing up on her Instagram a few weeks ago.
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