Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
Gradually mix the dry ingredients into the wet ingredients until just combined.
Fold in the chopped dried mango and shredded coconut until evenly distributed.
Drop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.