$\dfrac{1+ an^2 A}{1+\cot^2 A}$ equals to:

Question

$\dfrac{1+	an^2 A}{1+\cot^2 A}$ equals to:

Accepted Answer

Step 1: Use identities $1+	an^2A=\sec^2A$ and $1+\cot^2A=\mathrm{cosec}^2A$.
Step 2: $$\frac{1+	an^2A}{1+\cot^2A}=\frac{\sec^2A}{\mathrm{cosec}^2A}$$
Step 3: Write in terms of sine and cosine:
$$=\frac{1/\cos^2A}{1/\sin^2A}=\frac{\sin^2A}{\cos^2A}$$
Step 4: $\dfrac{\sin^2A}{\cos^2A}=	an^2A$.
Answer: (A) $	an^2 A$

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