What is the ruling of Sharia on a husband who divorced his wife with a single pronouncement during anger, then verbally and physically (by kissing her forehead) took her back during her waiting period (iddah) and without witnesses, and after the iddah ended, he informed his wife that he had taken her back, but the wife denied hearing the revocation? Is the revocation considered valid or not?

A revocable divorce allows the husband to take back his wife during her iddah (waiting period) without her consent or knowledge. The revocation is valid as soon as the husband pronounces it. However, if he does not explicitly pronounce the revocation but merely promises to take her back or kisses her forehead, the revocation is not effected thereby. If you inform your wife after her iddah has expired that you had taken her back, and she does not believe you, and you have no proof, then her word is to be accepted.