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: $\cot ^2 \mathrm{A}-\operatorname{cosec} \mathrm{A}$

Question : What is the value of $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$?

Option 1: $2 \sec \theta$

Option 2: $2 \operatorname{cosec} \theta$

Option 3: $2 \cot \theta$

Option 4: $\operatorname{cosec} \theta+\cot \theta$

Question : If $\operatorname{cosec} \theta-\cot \theta=\frac{7}{2}$, then the value of $\operatorname{cosec} \theta$ will be:

Option 1: $\frac{49}{28}$

Option 2: $\frac{21}{28}$

Option 3: $\frac{47}{28}$

Option 4: $\frac{53}{28}$

Question : If $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$, then the value of $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2 \theta}$ is:

Option 1: $\frac{16}{25}$

Option 2: $\frac{40}{41}$

Option 3: $\frac{41}{40}$

Option 4: $\frac{31}{30}$

Question : If $3 \operatorname{cosec} A=7$, then what is the value of $\cos A \tan A$?

Option 1: $\frac{2 \sqrt{10}}{7}$

Option 2: $\frac{3}{7}$

Option 3: $\frac{4}{7}$

Option 4: $\frac{\sqrt{10}}{7}$