已知函数$f_0\left(x\right)=\frac{\sin x}{x}(x>0)$，设$f_n\left(x\right)$为$f_{n-1}\left(x\right)$的导数，$n\in N^{*}$

（1）求$2f_1\left(\frac{\pi }{2}\right)+\frac{\pi }{2}{f}_2\left(\frac{\pi }{2}\right)$的值；
（2）证明：对任意$n\in N^{*}$，等式$\left|n{f}_{n-1}\left(\frac{\pi }{4}\right)+\frac{\pi }{4}{f}_n\left(\frac{\pi }{4}\right)\right|=\frac{\sqrt{2}}{2}$.