If period of function f(x)=cos(nx)sin5xn is 3π, then number of integral values of n must be
8
Given : Period of f(x)=cos(nx)sin(5xn) is 3π
∵f(x) is periodic ∴f(x+T)=f(x)
⇒cos(n(x+T))sin(5(x+T)n)=cos(nx)sin(5xn) (Where T=3π)
At x=0 cosnTsin(5Tn)=0
⇒cosnT=0 or sin5Tn=0
⇒nT=rπ+π2; rϵI or 5Tn=pπ; pϵI
Putting the value of T, we get,
⇒(3n−r)=12 which is not possible or 5×3πn=pπ⇒n=15p⇒p=±1,±3,±5,±15
So, number of integral values of n is 8.