Question : If $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$, then the value of $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2 \theta}$ is:

Option 1: $\frac{16}{25}$

Option 2: $\frac{40}{41}$

Option 3: $\frac{41}{40}$

Option 4: $\frac{31}{30}$

Question : If $\sin \theta+\cos \theta=\frac{1}{29}$, then find the value of $\frac{\operatorname{sin} \theta+\operatorname{cos} \theta}{\operatorname{sin} \theta-\operatorname{cos} \theta}$.

Option 1: $\frac{1}{41}$

Option 2: $\frac{43}{29}$

Option 3: $\frac{41}{29}$

Option 4: $\frac{1}{43}$

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: $2 \sqrt{3}$

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 : If $-\sin \theta+\operatorname{cosec} \theta=6$, then what is the value of $\sin \theta+\operatorname{cosec} \theta$ ?

Option 1: $6$

Option 2: $\sqrt{40}$

Option 3: $\sqrt{34}$

Option 4: $\sqrt{38}$