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For what integral value of n, is 3π the period of the function
cos(nx) sin(5x/n)
For a function to be periodic f(x+T) = f(x)
i.e. cos[n(x+T)]sin[5(x+T)/n]=cos(nx)sin(5x/n)
but period of a function is a positive real no. independent of x.
=>cos(nT)sin(5T/n)=0
CASE1
If cos(nT)=0 => nT=[(2K+1)PI/2] =>3PI(n) =[(2K+1)PI/2] =>(2K+1)=6n
=>3n-k=1/2 which is not possible as n and k both are integral values
CASE 2
sin(5T/n)=0 =>(5T/n) =(k)pi =>15/k=n
Now k is an integral value and thus n can attain 8 integral values ±1 ,±3 ,±5 ,±15
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