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

Option 1: $2 \cos A$

Option 2: $\sec A$

Option 3: $2\cos A$

Option 4: $2 \sec A$

Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.

Option 1: $\frac{7}{6 \sqrt{3}}$

Option 2: $\frac{\sqrt{3}}{6}$

Option 3: $\frac{7}{6}$

Option 4: $\frac{7}{2 \sqrt{3}}$

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 $\cos \theta=\frac{9}{13}$, then what is the value of $\operatorname{cosec} \theta$?

Option 1: $\frac{13}{\sqrt{22}}$

Option 2: $\frac{13 \sqrt{22}}{44}$

Option 3: $\frac{2 \sqrt{22}}{13}$

Option 4: $\frac{\sqrt{22}}{13}$

Question : If $\operatorname{cosec B} = \frac{3}{2}$, then what is the value of $\mathrm{\cot B \sin B} $?

Option 1: $\frac{\sqrt{5}}{3}$

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

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

Option 4: $\frac{2 \sqrt{5}}{3}$