# A geometry problem by cool dude

Geometry Level 4

$\large (\tan A - \cos B )^2 + ( \cot A - \sin B)^2$

Let $$A$$ and $$B$$ be real numbers. If the minimum value of the expression can be expressed as $$b - a \sqrt a$$, where $$a$$ and $$b$$ are positive integers, find the value of $$a+b$$.

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