(a) Show that \(\tan(r+1) - \tan r = \frac{\sin 1}{\cos(r+1)\cos r}\).

Let \(u_r = \frac{1}{\cos(r+1)\cos r}\).

(b) Use the method of differences to find \(\sum_{r=1}^{n} u_r\).

(c) Explain why the infinite series \(u_1 + u_2 + u_3 + \ldots\) does not converge.