JEE Math Practice Question

Let $$f: \mathbf{R} \rightarrow \mathbf{R}$$ be a function given by $$f(x)= \begin{cases}\frac{1-\cos 2 x}{x^2}, & x 0\end{cases}$$ where $$\alpha, \beta \in \mathbf{R}$$. If $$f$$ is continuous at $$x=0$$, then $$\alpha^2+\beta^2$$ is equal to :

1. A.48
2. B.6
3. C.3
4. D.12