sympathise vs empathise

sympathise and empathise both are verbs.

Word	Noun	Adjective	Verb	Adverb
sympathise	No	No	Yes	No
empathise	No	No	Yes	No

As verbs, sympathise and empathise are synonyms defined as:

Other synonyms of sympathise include empathize, sympathize, understand.

sympathise (verb)	empathise (verb)
be understanding of	be understanding of
to feel or express sympathy or compassion
share the feelings of; understand the sentiments of