To simplify the expression given:
1. Rewrite the expression: \( \frac{1}{\sec A - \tan A} - \frac{1}{\tan A + \sec A} \div 2\sec A \)
2. Find a common denominator for the fractions in the expression.
3. Combine the fractions using the common denominator.
4. Simplify further by performing the division by \( 2\sec A \).
By following these steps, you can simplify the given expression to a more manageable form for calculation and understanding.
