Question

Prove that cos√x is non periodic.

Answer 1

Solution

Let Cos(√x) be periodic with T as the period.

So, Cos(√x) = Cos{ √ (T+x) }

à √ (T+x) = 2nπ ± √x

Putting x = 0, we get, √T= 2nπ —–(1)

Putting x=T, we get √2T = 2nπ ± √T —-(2)

From (1) and (2) we get, √2T = √T ± √T

Or √T x √2 = √T (1 ± 1)

Or √2 = 1 ± 1, which is not possible, Hence Cos√x is not periodic function.