Answer
See the steps.
Work Step by Step
$LHS = \dfrac{\cos{(A+B)}}{\sin{A} \cos{B}} = \dfrac{\cos{A} \cos{B} - \sin{A} \sin{B}}{\sin{A} \cos{B}}$
$LHS = \dfrac{\cos{A}}{\sin{A}} - \dfrac{\sin{B}}{\cos{B}}$
$LHS = \cot{A} - \tan{B} = RHS$
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