Limits Continuity And Differentiability

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a function given by

$$f(x)= \begin{cases}\frac{1-\cos 2 x}{x^2}, & x < 0 \\ \alpha, & x=0, \\ \frac{\beta \sqrt{1-\cos x}}{x}, & x>0\end{cases}$$

where \(\alpha, \beta \in \mathbf{R}\). If \(f\) is continuous at \(x=0\), then \(\alpha^2+\beta^2\) is equal to :