any time i apply instant tan on my arms dark brown dry skin patches appear how to get rid of dry skin

Its because your skin is dry. I worked at a Tanning salon and any type of instant tanner will make dry skin appear patchy when applying because it’s drying over dried skin. Best advice I can give you is to exfoliate and moisturize every single day with a good body butter but only exfoliate twice a week and before applying the instant tanner.
A good home remedy you can use for dry skin is
6spoons of coffee
2 spoons of extra virgin Olive oil
1 whole egg
1 spoon of coconut oil
Mix it all in a bowl and when you are showering rub it on your skin it will exfoliate because of the coffee but it will also moisturize because of the olive oil the coconut oil and the egg. While you’re showering leave it on for around 10 minutes and then just to rinse it off. Your skin will feel so soft none oily and very moisturize.
hoped I helped