The value of $\left( an^{2}A-\dfrac{1}{\cos^{2}A} ight)$ is :

Question

The value of $\left(	an^{2}A-\dfrac{1}{\cos^{2}A}ight)$ is :

Accepted Answer

Step 1: Use $\dfrac{1}{\cos^{2}A}=\sec^{2}A$.
Step 2: The expression becomes
$$	an^{2}A-\sec^{2}A$$
Step 3: Apply the identity $1+	an^{2}A=\sec^{2}A$, i.e. $	an^{2}A-\sec^{2}A=-1$.
$$	an^{2}A-\sec^{2}A=-1$$
Correct option is (D) $-1$.

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