We define, for every non-zero natural number $n$, the function $k_{n}$ by
$$\begin{cases} k_{n}(x) = 1 - \frac{|x|}{n} & \text{if } |x| \leqslant n \\ k_{n}(x) = 0 & \text{otherwise} \end{cases}$$
We admit that $\int_{\mathbb{R}} \varphi = \pi$ where $\varphi(x) = \left(\frac{\sin x}{x}\right)^2$ for $x\neq 0$ and $\varphi(0)=1$. We set $K_{n} = \frac{1}{2\pi} \hat{k}_{n}$.\\
Show that the sequence of functions $\left(K_{n}\right)_{n \geqslant 1}$ is an approximate identity.