7. Calculate:
$$
\begin{array}{l}
\frac{1}{\sin 45^{\circ} \cdot \sin 46^{\circ}}+\frac{1}{\sin 46^{\circ} \cdot \sin 47^{\circ}}+ \\
\cdots+\frac{1}{\sin 89^{\circ} \cdot \sin 90^{\circ}} \\
=
\end{array}
$$
7. $\frac{1}{\sin 1^{\circ}}$.

Notice,
$$
\begin{array}{l}
\frac{1}{\sin n^{\circ} \cdot \sin (n+1)^{\circ}} \\
=\frac{1}{\sin 1^{\circ}} \cdot \frac{\sin \left[(n+1)^{\circ}-n^{\circ}\right]}{\sin n^{\circ} \cdot \sin (n+1)^{\circ}} \\
=\frac{1}{\sin 1^{\circ}} \cdot \frac{\sin (n+1)^{\circ} \cdot \cos n^{\circ}-\cos (n+1)^{\circ} \cdot \sin n^{\circ}}{\sin n^{\circ} \cdot \sin (n+1)^{\circ}} \\
=\frac{1}{\sin 1^{\circ}}\left[\cot n^{\circ}-\cot (n+1)^{\circ}\right] .
\end{array}
$$

Then the original expression
$$
\begin{array}{l}
=\sum_{k=45}^{89} \frac{1}{\sin 1^{\circ}}\left[\cot k^{\circ}-\cot (k+1)^{\circ}\right] \\
=\frac{1}{\sin 1^{\circ}}\left(\cot 45^{\circ}-\cot 90^{\circ}\right) \\
=\frac{1}{\sin 1^{\circ}} .
\end{array}
$$