Question : If $A=a \operatorname{cosec} \theta+b \cot \theta$ and $B=a \cot \theta+b \operatorname{cosec} \theta$, then what is the value of $A^2-B^2$?

Option 1: $ab$

Option 2: $(a+b)$

Option 3: $\left(a^2-b^2\right)$

Option 4: $(a-b)$

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 $0^{\circ}< \theta< 90^{\circ}$ 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: $3$

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

Option 1: $\sqrt2-\sqrt3$

Option 2: $\frac{\sqrt{2}(3+\sqrt{3})}{3}$

Option 3: $\frac{\sqrt{2}(3-\sqrt{3})}{3}$

Option 4: $\frac{3\sqrt{2}+\sqrt{3}}{3}$

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 $m = \sec \theta- \tan \theta$ and $n = \operatorname{cosec} \theta + \cot \theta$, then what is the value of $m + n(m-1)$?

Option 1: 2

Option 2: 1

Option 3: 0

Option 4: –1