# Find the period of the function f(x)=sin (pi x / n!) - cos (pi x / n+1!

Answers (1)

Solution:   We have ,

$f(x)=\sin \frac{\pi x}{n!}-\cos \frac{\pi x}{(n+1)!}$

$\\ \\ \sin \frac{\pi x}{n!}\rightarrow T_{1}=(\frac{2\pi}{\frac{\pi}{n!}}) =2n!\\ \\ \cos \frac{\pi x}{(n+1)!}\rightarrow T_{2}=(\frac{2\pi}{\frac{\pi}{(n+1)!}})=2(n+1)!\\ \\ \Rightarrow \hspace{1cm}T=2(n+1)!$

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