The period of the function f(x)=cos⁡πxn!−sin⁡πx(n+1)! is

Since sin x and cos x are periodic functions with period 2π.∴ Period of cos⁡πxn!=2ππ/n!=2(n!)  and period of sin⁡πx(n+1)!=2ππ/(n+1)!=2(n+1)!∴ Period of f (x) = L.C.M. of {2 (n!), 2 (n + 1)!} = 2 (n + 1)!