Capsaicin is defined in medical terms as the active component of chili peppers (genus Capsicum) that produces a burning sensation when it comes into contact with mucous membranes or skin. It is a potent irritant and is used topically as a counterirritant in some creams and patches to relieve pain. Capsaicin works by depleting substance P, a neurotransmitter that relays pain signals to the brain, from nerve endings.

Here is the medical definition of capsaicin from the Merriam-Webster's Medical Dictionary:

caпсаісіn : an alkaloid (C18H27NO3) that is the active principle of red peppers and is used in topical preparations as a counterirritant and analgesic.

Cosmetics are defined in the medical field as products that are intended to be applied or introduced to the human body for cleansing, beautifying, promoting attractiveness, and altering the appearance. According to the U.S. Food and Drug Administration (FDA), cosmetics include skin creams, lotions, makeup, perfumes, lipsticks, fingernail polishes, eye and facial makeup preparations, shampoos, permanent waves, hair colors, toothpastes, and deodorants, as well as any material intended for use as a component of a cosmetic product.

It's important to note that the FDA classifies cosmetics and drugs differently. Drugs are defined as products that are intended to diagnose, cure, mitigate, treat, or prevent disease, and/or affect the structure or function of the body. Some products, such as anti-dandruff shampoos or toothpastes with fluoride, can be considered both a cosmetic and a drug because they have both cleansing and therapeutic properties. These types of products are subject to regulation by both the FDA's Office of Cosmetics and Colors and its Center for Drug Evaluation and Research.

Cosmetics must not be adulterated or misbranded, meaning that they must be safe for use under labeled or customary conditions, properly packaged and labeled, and not contain any harmful ingredients. However, the FDA does not have the authority to approve cosmetic products before they go on the market, with the exception of color additives. Manufacturers are responsible for ensuring that their products are safe and properly labeled.