If the function

The function $f(x)=\left\{\begin{array}{cl}\frac{\sin ^{2} a x}{x^{2}}, & x \neq 0 \\ 1, & x=0\end{array}\right.$ is continuous at $x=0$.

$\therefore \lim _{x \rightarrow 0} f(x)=f(0)$

$\Rightarrow \lim _{x \rightarrow 0} \frac{\sin ^{2} a x}{x^{2}}=1$

$\Rightarrow a^{2}\left(\lim _{x \rightarrow 0} \frac{\sin a x}{a x}\right)^{2}=1$

$\Rightarrow a^{2} \times(1)^{2}=1 \quad\left(\lim _{x \rightarrow 0} \frac{\sin x}{x}=1\right)$

$\Rightarrow a^{2}=1$

$\Rightarrow a=\pm 1$

Thus, the value of $a$ is $\pm 1$.

If the function $f(x)=\left\{\begin{array}{cl}\frac{\sin ^{2} a x}{x^{2}}, & x \neq 0 \\ 1, & x=0\end{array}\right.$ is continuous at $x=0$, then $a=$ ___±1___.