doubt 3

Let cos x² be periodic
f(x+T)= f(x)
cos(x+T)²=cos x²
(x+T)²=2nπ±x²
x²+2Tx+T²Â±x²=2nÏ€
The above relation is not possible!!!
:)

y not possible ???plz explain

It is not possible because RHS is an integral multiple of 2Ï€ and LHS is a quadratic in x,

For eg. for x=0 and x=T,
T²=2nÏ€ and 4T²Â±T²

implies
4T²Â±T²=T²
4±1=1
Which is not possible:)