Question : If $\frac{21\cos A+3\sin A}{3\cos A+4\sin A}=2$, then find the value of cot A.

Option 1: $\frac{9}{11}$

Option 2: $\frac{11}{9}$

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

Option 4: $\frac{11}{10}$

Question : If $\sin \theta-\cos \theta=\frac{4}{5}$, then find the value of $\sin \theta+\cos \theta$.

Option 1: $ \frac{5}{\sqrt{34}} $

Option 2: $ \frac{5}{\sqrt{24}} $

Option 3: $ \frac{\sqrt{34}}{5} $

Option 4: $ \frac{\sqrt{24}}{5}$

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: $\frac{5}{13}$

Question : If $\tan\theta=1$, then the value of $\frac{8\sin\theta\:+\:5\cos\theta}{\sin^{3}\theta\:–\:2\cos^{3}\theta\:+\:7\cos\theta}$ is:

Option 1: $2$

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

Option 3: $3$

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

Question : If $\tan A=\frac{3}{8}$, then the value of $\frac{3 \sin A+2 \cos A}{3 \sin A-2 \cos A}$ is:

Option 1: $-\frac{13}{25}$

Option 2: $-\frac{25}{7}$

Option 3: $\frac{25}{8}$

Option 4: $\frac{13}{21}$