数学试题讲解

(1) 求证:

\frac{\sin 1^{\circ}}{\sin k^{\circ} \sin (k + 1)^{\circ}} = \frac{\cos k^{\circ}}{\sin k^{\circ}} - \frac{\cos (k + 1)^{\circ}}{\sin (k + 1)^{\circ}}

;
(2) 求值:

\frac{1}{\cos 0^{\circ} \cos 1^{\circ}} + \frac{1}{\cos 1^{\circ} \cos 2^{\circ}} + \dots + \frac{1}{\cos 44^{\circ} \cos 45^{\circ}}