ANOTHER vs. OTHER

ANOTHER comes from the combination AN + OTHER, so ANOTHER will be used in those cases where we would use A/AN, that is, before singular countable nouns.

For example, “Would you like a glass of water?” ---- “Would you like another glass of water?”

On the contrary, OTHER will be used in those cases where we wouldn’t use A/AN, that is, with the definite article THE, a possessive adjective (my, your, his …), SOME or ANY; or any plural countable or uncountable noun.

Some instances: “I left my wallet in my other trousers”; “Are you free any other day of the week?”