Question

The period of the function f(x)=sin 3x cos[3x]- cos 3xsin (3x), where [:] denotes the greatest integer function is
O 6
O 3
O 1/3
0 1/6​

Answer 1

Given :

f(x)=sin 3x cos[3x]- cos 3x sin [3x]

To find :

The greatest integer function

Solution:

f(x)=sin 3x cos[3x]- cos 3x sin [3x]

It is in the format of SinA CosB - CosA SinB = Sin (A -B )

    = sin (3x - [3x])

We know that x - [x] = {x}

f(x) ⇒ sin ( {3x} )

We know that period of {3x} is 1/3.

Therefore,

Period of f(x) = 1/3