Choose the correct value of $\dfrac{1+ an^2 A}{1+\cot^2 A}$.

Question

Choose the correct value of $\dfrac{1+	an^2 A}{1+\cot^2 A}$.

Accepted Answer

D. $	an^2 A$

Using identities, $1+	an^2 A=\sec^2 A$ and $1+\cot^2 A=\cosec^2 A$. So
$$\frac{1+	an^2 A}{1+\cot^2 A}=\frac{\sec^2 A}{\cosec^2 A}=\frac{1/\cos^2 A}{1/\sin^2 A}=\frac{\sin^2 A}{\cos^2 A}=	an^2 A.$$
Thus option D is correct.

Answer

$\sec^2 A$

Answer

$-1$

Answer

$\cot^2 A$

Choose the correct value of $\dfrac{1+\tan^2 A}{1+\cot^2 A}$.