Question

Choose the correct option. Justify your choice. $\frac{(1 + \text{tan}^2 A)}{(1 +\text{ cot}^ 2 A)}$

• A. sec2A
• B. -1
• C. cot2A
• D. tan2A

Answer 1

Answer: (D)

tan2A

Answer 2

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

$\frac{(1 + \text{tan}^2 A)}{(1 +\text{ cot}^ 2 A)}$ =$\frac{\left(1 + \frac{\text{sin}^2 A}{\text{cos}^2 A}\right) }{ \left(1 + \frac{\text{cos}^2 A}{\text{sin}^2 A}\right)}$

$=\frac{\frac{ \text{cos}^2 A + \text{sin}^2 A}{\text{cos}^2 A}}{\frac{\text{sin}^2 A + \text{cos}^2 A}{\text{sin}^2 A}}$

$= \frac{\frac{1}{\text{cos}^2 A}}{\frac{1}{\text{sin}^2 A}}$ [By using the identity: sin2 A + cos2 A = 1]

$= \frac{\text{sin}^2 A}{\text{cos}^2 A}$
= tan2 A
Hence, option (D) is correct.