The period of the function
`f(x)=cos2pi{2x}+ sin2 pi {2x}`,
is ( where {x} denotes the functional part of x)

Options

A. `1`
B. `(pi)/(2)`
C. `(1)/(2)`
D. `pi`

Answer

C

Explanation

We have,
`f(x)=cos2pi{2x}+ sin 2 pi{2x}`
`implies f(x)= cos2pi(2pi-[2x])+ sin2pi (2pi-[2x])`
`implies f(x)=cos(2pi[2x]-4pix)-sin(2pi[2x]-4pix)`
`implies f(x)= cos 4 x + sin 4 pi x " " [{:( :' cos (2npi-theta)= cos theta ),( sin (2n pi-theta)=- sin theta]`
Since ` cos 4 pi x ` and ` sin 4 pi x` are periodic functions each with period`(2pi)/(4pi)=(1)/(2)`.
Therefore, f(x) is periodicc with period `(1)/(2)`.