Answer
See the steps.
Work Step by Step
$RHS= \dfrac{2 \sec{A}}{\sec{A}-1}$
Multiplying by $\dfrac{\cos{A}}{\cos{A}}$
$RHS = \dfrac{2}{1-\cos{A}} = \dfrac{1}{\sin^2{\dfrac{A}{2}}} = \csc^2{\dfrac{A}{2}} = LHS$
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