Question

The period of the function f(x) = `cos(pi x/(n!))- sin(pix/((n+1)!))` is

Answer 1

Here, time period of `cos((pix)/(n!)) = 2n!`
Time period of `sin((pix)/((n+1)!)) = 2(n+1)!`
So, time period of `f(x)` will be the L.C.M. of the time period of the above two functions.
Time period will be the L.C.M. of `2n!` and `2(n+1)!`.
Now, `2n!` is a subset of `2(n+1)!`.
So, L.C.M. of `2n!` and `2(n+1)!` will be `2(n+1)!.`
`:.` Period of `f(x)` is ` 2(n+1)!`.