If cot α =$$\frac PQ$$​, then find the value of $$\frac{P \cos \alpha - Q \sin \alpha}{P \cos \alpha + Q \sin \alpha} - \frac{P^2 - Q^2}{P^2 + Q^2} + 3$$​​

Correct option is D

Given:
cot α = $$\frac PQ$$​
Formula Used:
​$$\cot \theta = \frac{\cos \theta}{\sin \theta}$$​​
Solution:
​$$\frac{P \cos \alpha - Q \sin \alpha}{P \cos \alpha + Q \sin \alpha} - \frac{P^2 - Q^2}{P^2 + Q^2} + 3\\\text{(Taking } \sin \alpha \text{ common in both numerator and denominator)}\\\frac{\sin \alpha (P \cot \alpha - Q)}{\sin \alpha (P \cot \alpha + Q)} - \frac{P^2 - Q^2}{P^2 + Q^2} + 3\\\text{(Putting value of } \cot \alpha = \frac{P}{Q})\\\\frac{\sin \alpha (P \frac{P}{Q} - Q)}{\sin \alpha (P \frac{P}{Q} + Q)} - \frac{P^2 - Q^2}{P^2 + Q^2} + 3\\\frac{\frac{P^2 - Q^2}{Q}}{\frac{P^2 + Q^2}{Q}} - \frac{P^2 - Q^2}{P^2 + Q^2} + 3\\\frac{P^2 - Q^2}{P^2 + Q^2} - \frac{P^2 - Q^2}{P^2 + Q^2} + 3\\= 3\\$$​​