Prove identity cos(x+2pi)=cosx

We'll apply the below identity to verify the given
expression:

cos (a+b) = cos a*cos b - sin b*sin
a

Let a = x and b = 2`pi`

cos (`x+ 2pi` ) = cos
x*cos `2pi` - sin `2pi` *sin x

But sin `2pi` = 0 and cos 2 =
1

cos (x+2`pi` ) = cos x*1 - 0*sin x

cos (x +
2`pi` ) = cos x

Therefore, the given identity cos
(x+2`pi` ) = cos x is demonstrated.