The area under arms has become dark due to the constant use of hair-removing cream and razors.
Use this skin-lightening remedy:
Mix gram flour (equal quantities of Green Gram and Bengal Gram) with milk or rice water.

Scrub the paste on the affected area, and rinse with clear water.

Use a good quality sunscreen (SPF 30) daily.

Opt for waxing. This will ensure that your skin does not become darker than it already is.