Question 14
Let $A$, $B$ and $C$ be real numbers such that
(i) $\sin A \cos B + |\cos A \sin B| = \sin A |\cos A| + |\sin B \cos B|$,
(ii) $\tan C$ and $\cot C$ are defined.
Find the minimum value of $(\tan C - \sin A)^2 + (\cot C - \cos B)^2$.
(i) $\sin A \cos B + |\cos A \sin B| = \sin A |\cos A| + |\sin B \cos B|$,
(ii) $\tan C$ and $\cot C$ are defined.
Find the minimum value of $(\tan C - \sin A)^2 + (\cot C - \cos B)^2$.