Question

The period of cos CM0/2 ) is​

Answer 1

Answer:

A function is periodic if f(x)=f(x+T).

Let us assume that cos(x

2

) has a period of T. In that case:

cos(x+T)

2

=cosx

2

⇒(x+T)

2

=2nπ+x

2

⇒x

2

+T

2

+2xT=2nπ+x

2

⇒T

2

+2xT−2nπ=0

As we can see, T is dependent on the value of x and hence, is not a constant.

So cos(x

2

) is not periodic.

So, we can say that period of cos(x

2

) does not exist

I think so it is correct