​$$\frac{1 + \tan^2 A}{1 + \cot^2 A} = \, \text{------}$$​​

Correct option is D

Given:

$$\frac{1 + \tan^2 A}{1 + \cot^2 A}$$

Formula used:

$$\sec^2 A = 1 + \tan^2 A$$​

$$\cosec^2 A = 1 + \cot^2 A$$​​

Solution:

​$$\frac{1 + \tan^2 A}{1 + \cot^2 A}$$

$$= \frac{\sec^2 A}{\cosec^2 A}$$​​

= $$\frac{\left(\frac{1}{\cos^{2} A}\right)}{\left( \frac{1}{\sin^{2} A}\right)}$$​

= $$\frac{1}{\cos^{2} A}\times {\sin^{2} A}$$​​

= $$\frac{\sin^{2} A}{\cos^{2} A}$$​

= $$\tan^{2} A$$

Thus, the correct answer is (d).