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 $\cos A+\cos^2 A=1$, then the value of $\sin^4 A+\sin^6 A$ is:

Option 1: $2$

Option 2: $\cos \mathrm{A}$

Option 3: $1$

Option 4: $\sin A$

Question : Which of the following options gives an expression equivalent to $\sin \ (A + B)$?

Option 1: $\cos\ A \cos\ B - \sin \ A \sin \ B$

Option 2: $\sin\  A \cos \ B + \cos\ A\ \sin \ B$

Option 3: $\cos \ A \cos\ B+\sin\ A \sin \ B$

Option 4: $\sin \ A \cos \ B - \cos \ A \sin \ B$

Question : Solve the following to find its value in terms of trigonometric ratios.
$(\sin A + \cos A)(1 - \sin A \cos A)$

Option 1: $\sin^3A+\cos^3A$

Option 2: $\sin^2A-\cos^2A$

Option 3: ${[\cos A-\sin A]\left[\sin ^2 A+\cos ^2 A\right]}$

Option 4: $\sin^3A-\cos^3A$

Question : Find the value of the following expression.
$5\left(\sin ^4 \theta+\cos ^4 \theta\right)+3\left(\sin ^6 \theta+\cos ^6 \theta\right)+19 \sin ^2 \theta \cos ^2 \theta$

Option 1: 8

Option 2: 5

Option 3: 6

Option 4: 7