Question : If $\sin A=\frac{1}{2}$, then the value of $(\tan A+\cos A)$ is:

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

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

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

Option 4: $\frac{5}{3 \sqrt{3}}$

Question : If $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$, then the value of A is:

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

Option 2: $\frac{3}{10}$

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

Option 4: $\frac{1}{10}$

Question : If $3A=5B$, what is the value of $\frac{A+B}{B}$?

Option 1: $\frac{8}{3}$

Option 2: $\frac{8}{5}$

Option 3: $\frac{5}{8}$

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

Question : If $a-\frac{1}{a}=4$, then the value of $a+\frac{1}{a}$ is:

Option 1: $5 \sqrt{5}$

Option 2: $4 \sqrt{5}$

Option 3: $2 \sqrt{5}$

Option 4: $3 \sqrt{5}$

Question : If $\alpha$ is an acute angle and $2\sin \alpha+15\cos^2\alpha=7$, then the value of $\cot \alpha$ is:

Option 1: $\frac{4}{3}$

Option 2: $\frac{4}{5}$

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

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