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 $\sin\theta+\cos\theta=\sqrt{2}\cos\theta$, then the value of $\cot\theta$ is:

Option 1: $\sqrt{2}+1$

Option 2: $\sqrt{2}-1$

Option 3: $\sqrt{3}-1$

Option 4: $\sqrt{3}+1$

Question : If $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is:

Option 1: $\frac{\sqrt{15}-1}{8}$

Option 2: $\frac{\sqrt{15}-1}{4}$

Option 3: $\frac{\sqrt{15}+1}{4}$

Option 4: $\frac{\sqrt{15}-1}{2}$

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 $\sin \theta \cos \theta=\frac{1}{\sqrt{3}}$ then the value of $\left(\sin ^4 \theta+\cos ^4 \theta\right)$ is:

Option 1: $1$

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

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

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