Question : If $\cot \theta=\frac{9}{17}$, find the value of $\operatorname{cosec}^2 \theta$.

Option 1: $1\frac{9}{17}$

Option 2: $\frac{208}{289}$

Option 3: $\frac{8}{17}$

Option 4: $1\frac{81}{289}$

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 $\operatorname{cosec} \theta=\frac{17}{15}$, then what will be the value of $\cos \theta?$

Option 1: $\frac{7}{17}$

Option 2: 1

Option 3: $\frac{8}{17}$

Option 4: $\frac{15}{17}$

Question : If $6 \sec \theta=10$, then find the value of $\frac{5 \operatorname{cosec} \theta-3 \cot \theta}{4 \cos \theta+3 \sin \theta}$.

Option 1: $\frac{2}{3}$

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

Option 3: $\frac{5}{6}$

Option 4: $\frac{6}{5}$

Question : If $0^{\circ}< \theta< 90^{\circ}$ and $\operatorname{cosec \theta} =\cot^{2}\theta$, then the value of expression $\operatorname{cosec^{4}\theta}–\operatorname{2cosec^{2}\theta}-\cot^{2}\theta$ is equal to:

Option 1: $2$

Option 2: $0$

Option 3: $1$

Option 4: $3$