Question

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

• A. ${\sec }^{2}A$
• B. $-1$
• C. ${\cot }^{2}A$
• D. ${\tan }^{2}A$

Answer 1

The correct option is D ${\tan }^{2}A$

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

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

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

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