Home
Class 12
MATHS
The period of the function f(x) = cos(pi...

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

Text Solution

Verified by Experts

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)!`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The period of the function f(x)=sin((pi x)/((n+1)!))-sin((pi x)/(n!)) is given by (i) 2(n!) (ii) 2((n+1)!)( iii) 2 pi (iv) 2(n(n+1)!)

The period of the fuction f(x)=sin""((pix)/(n!))+ cos((pix)/((n+1)!)) , is

The period of the fuction f(x)=sin""((pix)/(n!))+ cos((pix)/((n+1)!)) , is

The period of the fuction f(x)=sin""((pix)/(n!))+ cos((pix)/((n+1)!)) , is

The function f(x)=sin""(pix)/(n!)-cos""(pix)/((n+1)!) is :

Period of the function f(x) = sin((pi x)/(2)) cos((pi x)/(2)) is

Period of the function f(x) = sin((pi x)/(2)) cos((pi x)/(2)) is

Find the period of the function f(x)=3sin((pi x)/(3))+4cos((pi x)/(4))

The period of the function : f(x)=3sin""(pix)/(3)+4cos""(pix)/(4) is :

Find the period of the function f(x) = sin((pi x)/3) + cos ((pi x)/2) .