Question : What is the value of the given expression if $3\cot A=\frac{7}{3}$?
$\frac{3 \cos A+2 \sin A}{3 \cos A-2 \sin A}$

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

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

Option 3: $13$

Option 4: $1$

Question : If $\frac{\sin x-\cos x}{\sin x+\cos x}=\frac{2}{5}$, then the value of $\frac{1+\cot ^2 x}{1-\cot ^2 x}$ is:

Option 1: 2.25

Option 2: 1.45

Option 3: 3.75

Option 4: 5.25

Question : If $\sin t+\cos t=\frac{4}{5}$, then find $\sin t.\cos t$.

Option 1: $\frac{9}{50}$

Option 2: $-\frac{9}{50}$

Option 3: $\frac{9}{25}$

Option 4: $-\frac{9}{25}$

Question : If $4 \tan \theta=3$, then $\frac{4 \sin \theta-\cos \theta+1}{4 \sin \theta+\cos \theta-1}=?$

Option 1: $\frac{14}{11}$

Option 2: $\frac{12}{11}$

Option 3: $\frac{10}{11}$

Option 4: $\frac{13}{11}$

Question : If $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}=\frac{3}{2}$, then the value of $\sin ^4 \theta-\cos ^4 \theta$ is:

Option 1: $\frac{5}{12}$

Option 2: $\frac{12}{13}$

Option 3: $\frac{11}{12}$

Option 4: $\frac{5}{13}$