What are the steps in order to transform the cosine function to the exponential function:
$$ \left[\cos \left(\frac{k \pi} N\right)\right]^n \approx e ^ {\frac{-n}2 \left(\frac{k \pi} N \right)^2} $$ if I know that $$ 0 < k/N \ll 1 $$
I just want to understand this step. I am aware of the Euler's formula, yet I can't figure out, how to use it. The article I am reading is here