Given that a is a non 0 real number and ck is a series of real number for all k natural number where $\sum_{k= 1}^{\infty} c_k^2 = \infty $. If $c_k \to 0$, proof that $lim _{n \to \infty}\prod_{k=1}^{n}cos(ac_k) = 0$
My question is, how can I translate $cos(ac_k)$ into $c_k^2$? It seems like I need to use imaginary number (euclid theorem) to solve this but I m not sure. Thank you.