The period of the function `f(x)=4sin^(4) ((4x-3pi)/(6pi^(2)))+2 cos ((4x-3pi)/(3pi^(2)))` is

Options

A. ` ( 3pi ^(2))/( 4)`
B. `( 3pi ^(3))/( 4)`
C. ` ( 4pi ^(2))/( 3)`
D. ` ( 4pi^(3))/( 3)`

Answer

B

Explanation

We have,
`f(x) = 4 sin^(4)((2)/(3pi^(2))x-(1)/(2pi))+ 2 cos((4x -6pi)/(2pi^(2)))`
We Know that `sin^(4)x` and `cos^(4)x` are periodic functions with
period`(pi)/(2)`. Therefore, `4sin^(4)((2)/(3pi^(2))x-(1)/(2pi))` and `2 cos^(4)((2)/(pi^(2))x-(3)/(pi))`
are periodic with periodic `(3pi^(3))/(4)` and `(pi^(3))/(4)` respectively.
Hence f(x) is periodic with period `(3pi^(3))/(4)`.