If $${\text{cos}}\theta = \frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}$$    then the value of$${\text{cot}}\theta $$  is equal to $$\left[ {{\text{if }}{0^ \circ } \leqslant \theta \leqslant {{90}^ \circ }} \right]$$

A. $$\frac{{2xy}}{{{x^2} - {y^2}}}$$

B. $$\frac{{2xy}}{{{x^2} + {y^2}}}$$

C. $$\frac{{{x^2} + {y^2}}}{{2xy}}$$

D. $$\frac{{{x^2} - {y^2}}}{{2xy}}$$

Answer: Option D

Solution(By Examveda Team)

$${\text{cos}}\theta = \frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}$$

AC² = (x² + y²)² - (x² - y²)²
        = x⁴ + y⁴ + 2x²y² - x⁴ - y⁴ + 2x²y²
        = 4x²y²
⇒ AC = 2xy
⇒ cotθ = $$\frac{{{x^2} - {y^2}}}{{2xy}}$$