Question : Simplify the given equation: $\frac{\cot^3A–1}{\cot A–1}$
Option 1: $\operatorname{cosec}^2 \mathrm{A}-\cot \mathrm{A}$
Option 2: $\operatorname{cosec}^2 A+\cot A$
Option 3: $\cot ^2 \mathrm{A}+\operatorname{cosec} \mathrm{A}$
Option 4: $\cot ^2 \mathrm{A}-\operatorname{cosec} \mathrm{A}$
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Correct Answer: $\operatorname{cosec}^2 A+\cot A$
Solution : Given: $\frac{\cot^3A–1}{\cot A–1}$ = $\frac{(\cot A–1)(\cot^2A+\cot A+1)}{(\cot A–1)}$ = $\cot^2A+\cot A+1$ = $\operatorname{cosec^2}A+\cot A$ Hence, the correct answer is $\operatorname{cosec}^2 A+\cot A$.
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