Let x = sin1^o then the value of the expression $\frac{1}{\cos 0^0\cdot \cos 1^0}+\frac{1}{\cos 1^0\cdot \cos 2^0}+\frac{1}{\cos 2^0,\cos 3^0}+\dots \dots ..+\frac{1}{\cos {44}^0\cdot \cos {45}^0}$ is equal to 

$\begin{array}{l}\frac{1}{\sin 1^0}\left[\frac{\sin \left(2^0-1^0\right)}{\cos 0^0\cos 1^0}+\frac{\sin \left(2^0-1^0\right)}{\cos 1^0\cos 2^0}+\frac{\sin \left(3^0-2^0\right)}{\cos 2^0\cos 3^0}+\dots ..+\frac{\sin \left({45}^{\circ }-{44}^0\right)}{\cos {44}^0\cos {45}^0}\right]\\ =\frac{1}{\sin 1^0}\left[\tan 1^0+\left(\tan 2^0-\tan 1^0\right)+\left(\tan 3^0-\tan 2^{\circ }\right)+\left(\tan 4^0-\tan 3^{\circ }\right)+\dots ..+\left(\tan {45}^{\circ }-\tan {44}^{\circ }\right)\right]\\ =\frac{1}{\sin 1^0}=\frac{1}{\mathrm{x}}\end{array}$