The value of  $$\frac{(1+tan^2⁡θ)}{(1+cot^2⁡θ )}\text{ is:}$$​​

Correct option is A

Given:

$$\frac{(1 + \tan^2 \theta)}{(1 + \cot^2 \theta)}$$​

Formula Used:

$$1 + \tan^2 \theta = \sec^2 \theta \\1 + \cot^2 \theta = \cosec^2 \theta$$​

Solution:

$$\frac{(1 + \tan^2 \theta)}{(1 + \cot^2 \theta)} \\= \frac{\sec^2 \theta}{\cosec^2 \theta}\\ = \frac{1/\cos^2 \theta}{1/\sin^2 \theta}\\ = \frac{\sin^2 \theta}{\cos^2 \theta}\\= \tan^2 \theta$$​