1. **State the problem:** Calculate the limit $$\lim_{x \to 0} \frac{1 - \cos^2 x}{x^2}$$. 2. **Recall the identity:** Note that $$1 - \cos^2 x = \sin^2 x$$ by the Pythagorean identity. 3. **Rewrite the limit:** Substitute to get $$\lim_{x \to 0} \frac{\sin^2 x}{x^2}$$. 4. **Use limit properties:** This can be written as $$\lim_{x \to 0} \left( \frac{\sin x}{x} \right)^2$$. 5. **Evaluate the known limit:** We know $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$. 6. **Calculate the final limit:** Therefore, $$\lim_{x \to 0} \left( \frac{\sin x}{x} \right)^2 = 1^2 = 1$$. **Final answer:** $$\boxed{1}$$