The fundamental period of the function `f(x)=4cos^4((x-pi)/(4pi^2))-2cos((x-pi)/(2pi^2))` is equal to :

Explanation

`f(x)=4"cos"^(4)((x-pi)/(4pi^(2)))-2 "cos"((x-pi)/(2pi^(2)))`
`=(2"cos"^(2)((x-pi)/(4pi^(2))))^(2)-2 "cos"((x-pi)/(2pi^(2)))`
`=(1+"cos"((x-pi)/(2pi^(2))))^(2)-2 "cos"((x-pi)/(2pi^(2)))`
` " "("using "2cos^(2) theta=1+cos 2 theta)`
`="cos"^(2)((x-pi)/(2pi^(2)))+1`
`=(1+"cos"((x-pi)/(pi^(2))))/(2)+1`
`=("cos"((x)/(pi^(2))-(1)/(pi))+3)/(2)`
` :. ` Period of f(x) is `(2pi)/((1)/(pi^(2)))=2pi^(3)`