$\frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\frac{1}{\sin 3^{\circ} \sin 4^{\circ}}+\ldots+\frac{1}{\sin 89^{\circ} \sin 90^{\circ}} = ?$

• A
  $\frac{\sin 1^{\circ}}{\tan 1^{\circ}}$
• B
  $\frac{1}{\sin ^2 1^{\circ}}$
• C
  $\frac{\cot 1^{\circ}}{\sin 1^{\circ}}$
• D
  $\frac{\tan 1^{\circ}}{\cos 1^{\circ}}$