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

Question : If $\operatorname{cosec} \theta=1 \frac{7}{22}$, then find the value of $\cot ^2 \theta$.

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:

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

Question : If $\theta$ is a positive acute angles and $\operatorname{cosec}\theta =\sqrt{3}$, then the value of $\cot \theta -\operatorname{cosec}\theta$ is: