uncover: to remove sth that is covering sth;to discover sth that was previously hidden or secret.

主要指移去遮盖物让东西显露出来，也可指揭露阴谋秘密等。

eg: Please uncover the saucepan.

    The police have uncovered a plot.警察当局侦破了一起阴谋。

expose: to tell the true facts about a person or a situation, and show them/it to be immoral,illegal；to show sth that is usually hidden.

多指揭露丑闻，坏人坏事或各种阴谋。也可指某物暴露在外。

eg: He smiled suddenly, exposing a set of amazingly white teeth.

I will expose his all lawless action.

disclose: to give sb information about sth,especially sth that was previously secret.

侧重指揭露或泄露鲜为人知或保密的事。

eg: Science can disclose the mysteries of nature.

    It was suggested that all government ministers should disclose information on their financial interests.

reveal: to make sth known to sb. 多指揭露一直隐藏或隐秘的东西。

eg: These few words fully revealed her noble quality.