The value of $\left(\cot^{2}A-\dfrac{1}{\sin^{2}A}\right)$ is :

Question

Accepted Answer

Step 1: Use $\dfrac{1}{\sin^{2}A}=\operatorname{cosec}^{2}A$.
Step 2: The expression becomes
$$\cot^{2}A-\operatorname{cosec}^{2}A$$
Step 3: Apply the identity $1+\cot^{2}A=\operatorname{cosec}^{2}A$, so $\cot^{2}A-\operatorname{cosec}^{2}A=-1$.
$$=-1$$
Correct option is (D) $-1$.

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