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 $\operatorname{tan} \theta=\frac{3}{4}$, then find the value of expression $\frac{1+\operatorname{sin} \theta}{1-\operatorname{sin} \theta}$.

Option 1: 4

Option 2: 3

Option 3: 8

Option 4: 5

Question : What is the value of $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}+\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}$?

Option 1: $\frac{1}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$

Option 2: $2\left(\sin ^2 \theta-\cos ^2 \theta\right)$

Option 3: $\frac{2}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$

Option 4: $\sin ^2 \theta-\cos ^2 \theta$

Question : If $\sin \theta-\cos \theta=\frac{1}{5}$, then find the value of $\sin \theta+\cos \theta$.

Option 1: $\frac{5}{7}$

Option 2: $\frac{7}{5}$

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

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

Question : If $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=3$, then the value of $\sin^{4}\theta$ is:

Option 1: $\frac{2}{5}$

Option 2: $\frac{1}{5}$

Option 3: $\frac{16}{25}$

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