The value of $$\left(\frac{sinA}{1-cosA} + \frac{1-cosA}{sinA}\right) \div \left(\frac{cot^2A}{1+cosecA} + 1\right)$$ is:

$$\left(\frac{sinA}{1-cosA} + \frac{1-cosA}{sinA}\right) \div \left(\frac{cot^2A}{1+cosecA} + 1\right)$$
Let the value of $$\theta = 45\degree$$,
$$\left(\frac{\frac{1}{\sqrt{2}}}{1- \frac{1}{\sqrt{2}}} + \frac{1- \frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}\right) \div \left(\frac{1}{1+\sqrt{2}} + 1\right)$$

=$$\left(\frac{\frac{1}{2} + (1- \frac{1}{\sqrt{2}})^2}{(\frac{1}{\sqrt{2}})(1- \frac{1}{\sqrt{2}})}\right) \div \left(\frac{1 + 1+\sqrt{2}}{1+\sqrt{2}}\right)$$

= $$\left(\frac{\frac{1}{2} + 1 + \frac{1}{2} - \sqrt{2}}{(\frac{1}{\sqrt{2}})(1- \frac{1}{\sqrt{2}})}\right) \div \left(\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)$$

= $$\left(\frac{2 - \sqrt{2}}{(\frac{1}{\sqrt{2}}- \frac{1}{2})}\right) \div \left(\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)$$

= $$\left(\frac{2 - \sqrt{2}}{\frac{2 - \sqrt{2}}{2\sqrt{2}}}\right) \div \left(\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)$$

= $$2\sqrt{2} \times \frac{1+\sqrt{2}}{2+\sqrt{2}}$$ = 2