Question : If $\frac{1}{\operatorname{cosec} \theta+1}+\frac{1}{\operatorname{cosec} \theta-1}=2 \sec \theta, 0^{\circ}<\theta<90^{\circ}$, then the value of $\frac{\tan \theta+2 \sec \theta}{\operatorname{cosec} \theta}$ is:

Option 1: $\frac{4+\sqrt{2}}{2}$

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

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

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

Question : The value of $\sqrt{\frac{1+\sin A}{1-\sin A}}$ is:

Option 1: $\sec A-\tan A$

Option 2: $\operatorname{cosec} A+\cot A$

Option 3: $\sec A+\tan A$

Option 4: $\operatorname{cosec} A-\cot A$

Question : If $7 \sin ^2 \theta+3 \cos ^2 \theta=4,0^{\circ}<\theta<90^{\circ}$, then the value of $(\tan ^2 2 \theta+\operatorname{cosec}^2 2 \theta)$ is:

Option 1: $7$

Option 2: $\frac{15}{4}$

Option 3: $\frac{13}{3}$

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

Question : If $(\operatorname{cosec} \theta-\cot \theta) = \frac{7}{2}$, the value of $\operatorname{cosec} \theta$ is:

Option 1: $\frac{47}{28}$

Option 2: $\frac{51}{28}$

Option 3: $\frac{53}{28}$

Option 4: $\frac{49}{28}$

Question : If $\frac{\cos \theta}{1-\sin \theta}+\frac{\cos \theta}{1+\sin \theta}=4,0^{\circ}<\theta<90^{\circ}$, then what is the value of $(\sec \theta+\operatorname{cosec} \theta+\cot \theta) ?$

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

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

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

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