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You've made one thing wrong — it's the bot, not you, that selects the escape angle. if the bot move perpendicular to you, and your bullet speed is the same — you will not hit him definitely. Whatever formula you use, the fact of not being able to hit will never change, in this case. Therefore it still can't prove it's wrong.

The only way to prove asin formula is wrong is by giving a formula that is greater than or equal to asin formula all the time (and that formula must satisfy the game physics as well)