1. **State the problem:** Simplify the expression $$\frac{\sec^2 x - 1}{\sin^2 x}$$ and identify it as a single trigonometric identity. 2. **Recall relevant identities:** - $$\sec^2 x = 1 + \tan^2 x$$ (Pythagorean identity) - $$\sin^2 x = 1 - \cos^2 x$$ (basic identity) 3. **Substitute $$\sec^2 x$$:** $$\frac{\sec^2 x - 1}{\sin^2 x} = \frac{(1 + \tan^2 x) - 1}{\sin^2 x} = \frac{\tan^2 x}{\sin^2 x}$$ 4. **Express $$\tan^2 x$$ in terms of sine and cosine:** $$\tan^2 x = \frac{\sin^2 x}{\cos^2 x}$$ 5. **Substitute into the expression:** $$\frac{\tan^2 x}{\sin^2 x} = \frac{\frac{\sin^2 x}{\cos^2 x}}{\sin^2 x}$$ 6. **Simplify the complex fraction:** $$= \frac{\sin^2 x}{\cos^2 x} \times \frac{1}{\sin^2 x} = \frac{\cancel{\sin^2 x}}{\cos^2 x} \times \frac{1}{\cancel{\sin^2 x}} = \frac{1}{\cos^2 x}$$ 7. **Recognize the final expression:** $$\frac{1}{\cos^2 x} = \sec^2 x$$ **Final answer:** The expression simplifies to $$\sec^2 x$$. Therefore, the correct choice is **sec^2 x**.