Let $C(\theta)=\displaystyle\sum _{n=0}^{\infty}\dfrac{\cos(n\theta)}{n!}$

Which of the following statements is FALSE?

$C(0)=e$

$C(\pi)=\dfrac{1}{e}$

Hence, option A and B are correct

$C'(\theta)= -\displaystyle \sum_{n=0}^{\infty }\dfrac{\sin\theta }{(n-1)!}$

$C'(\theta)=0$

Therefore, option D is false because $C'(\theta) =0$ for $n=0$