Prove that $\sum_{n=1}^{\infty}\frac{|\cos n|}{n}$ diverges

Question

Prove that the series $\displaystyle \sum_{n=1}^{\infty}\frac{|\cos n|}{n}$ diverges.

I knew that the series $\displaystyle \sum_{n=1}^{\infty}\frac{|\sin n|}{n}$ diverges, but it seems the proof for the case of sine cannot be applied to the case of cosine.

Thanks so much.