In Chamber of Secrets, in the first Duelling Club class, Snape suggests Malfoy use the Serpensortia spell against Harry. This of course reveals that Harry is a Parselmouth, but how could Snape anticipate this? Was there any reason for Snape to suspect Harry is a Parselmouth? Or was it just a way to laugh at how Harry would get frightened?
First, it's not definite that Snape told Draco to use Serpensortia. All that we know is that he said quietly something to Draco before the duel.
Snape moved closer to Malfoy, bent down, and whispered something in his ear. Malfoy smirked, too.
It could have been something as simple as "hit him hard and fast. Keep him on his back feet" or "50 points to Slytherin if you defeat him in a suitable humiliating way". Secondly, the spell may have its own uses, whether on a direct combat level (the books and movies are hazy on whether magical shielding blocks physical attacks, or if the shielding is directional, possibly allowing the snake to provide a flanking attack) or simply on a psychological level, forcing the opponent to split their attention.
We do know that Snape enjoyed Harry's discomfort
"Don't move, Potter," said Snape lazily, clearly enjoying the sight of Harry standing motionless, eye to eye with the angry snake. "I'll get rid of it ......
And that the event led Snape to realize or decide something
Snape, too, was looking at Harry in an unexpected way: It was a shrewd and calculating look, and Harry didn't like it.
It is possible that Snape suggested that Malfoy use the spell to ferret out that Harry was a parselmouth, but there is no textual evidence that he even suspected.