Question : If $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$, then the positive value of $\cot \theta+\cos \theta$ is:

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

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

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

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

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

Question : If $\mathrm{A}=\cot 30^{\circ} \tan 60^{\circ}+\cot 60^{\circ} \tan 30^{\circ}$, then what is the value of A?

Option 1: $\frac{1}{ \sqrt{ 3}}$

Option 2: $\frac{10}{3}$

Option 3: $\frac{10}{ \sqrt{3}}$

Option 4: $\frac{1}{3}$

Question : If $\sqrt{2} \sec ^2 \theta-4 \sec \theta+2 \sqrt{2}=0$, then what is the value $\sin ^2 \theta+\tan ^2 \theta$?

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

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

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

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

Question : If $\cos \theta+\sec \theta=\sqrt{3}$, then the value of $\cos ^3 \theta+\sec ^3 \theta$ is:

Option 1: $0$

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

Option 3: $\sqrt{3}$

Option 4: $2 \sqrt{3}$