Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

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