The function f(x)= sinπxn!-cosπx(n+1)! is

Since the period of sin x is 2π so the period of sin πxn! is 2πn!π=2(n!) The period of cosπx(n+1)! is 2(n+1)! The period of f(x)=1.c.m (2n!),2(n +1)!=2(n+1)!