Question : If $\sin \theta=\frac{5}{13}$, then what is the value of $\frac{\cos ^{2} \theta-\sin ^{2} \theta}{2 \cos \theta \cdot \sin \theta}?$

Option 1: $\frac{117}{136}$

Option 2: $\frac{113}{120}$

Option 3: $\frac{115}{126}$

Option 4: $\frac{119}{120}$

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: $\frac{3}{5}$

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 $\sin \theta \cos \theta=\frac{1}{\sqrt{3}}$ 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: $\frac{1}{3}$

Question : If $\sin \theta \cos \theta=\frac{\sqrt{2}}{3}$,then the value of $\left(\sin ^6 \theta+\cos ^6 \theta\right)$ is:

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

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

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

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

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