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 $\tan \theta=\frac{8}{15}$, then the value of $\sqrt{\frac{1-\sin \theta}{1+\sin \theta}}$ is:

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

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

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

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

Question : If $6 \sec \theta=10$, then find the value of $\frac{5 \operatorname{cosec} \theta-3 \cot \theta}{4 \cos \theta+3 \sin \theta}$.

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

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

Option 3: $\frac{5}{6}$

Option 4: $\frac{6}{5}$

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 $\sin \theta-\cos \theta=0$, then what is the value of $\sin ^2 \theta+\tan ^2 \theta$ ?

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

Option 2: $1$

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

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