Correct spelling


Correct spelling, explanation: coolly is an adverb formed from the adjective cool. The rule says that making adverbs from adjectives, we add the suffix ly to the end of the related word. For example, slowslowly, clevercleverly, bravebravely, which shows that from cool it should be coolly, not cooly. It is very easy to memorize this unexceptional adverb. As a result, coolly is the correct spelling, and cooly not.

Definition of coolly:
adverb, people who act coolly do something in an unfriendly way that lacks enthusiasm or interest,
He eyed her coolly and answered in a dry tone.
They found out that this crime had been premeditated coolly.

Incorrect spelling


Incorrect spelling, explanation: there is the rule that says when adverbs are created from adjectives, the ending ly is added to them. Coolly is a derivation from the adjective cool and therefore cooly is inapropriate form, where one consonant l is missing. Hence, coolly is the correct spelling, but cooly is wrong.