The hair is just a coincidence. A tan is what happens when UV in sunlight hits our skin. It damages it a little bit (or a lot in the case of a sunburn) and your skin produces a chemical called melanin in response to try and protect itself. That increase in melanin darkens your skin and is a tan. But as new skin cells are made and the old ones slough off the new skin cells haven’t been exposed to UV and so only have your normal amount of melanin in them and your skin looks lighter again. So places like your hands and face where your body replaces your skin cells very quickly lose their tan very quickly, and places where your body doesn’t make new skin as fast like your shoulders keeps the tan for longer. So it’s about how fast your body replaces skin cells not about body hair.
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