real analysis - How do I evaluate this limit :$displaystyle lim_{xto infty} (1+cos x)^frac{1}{cos x}$?

I would like to know if this :$$ \lim_{x\to \infty} (1+\cos x)^\frac{1}{\cos x}$$ does exist and how do i evaluate it ?.

Note : I have tried to use the standard limit : $$ \lim_{z\to \infty} \left(1+\frac{1}{z}\right)^z=e$$ using $\cos x=1/z $ but i can't
succeed

Thank you for any help .

Answer

For any natural number $n$, if $x=2n\pi$ ,the value of the function is 2; if $x=(2n+1/2)\pi$, the value is 1. So no convergence.