Question : Find the value of $\sqrt{\frac{1-\tan A}{1+\tan A}}$.

Option 1: $\sqrt{\frac{1+\sin 2 A}{\cos 2 A}}$

Option 2: $\sqrt{\frac{1-\sin 2 A}{\cos 2 A}}$

Option 3: $\sqrt{\frac{1+\sin A}{\cos A}}$

Option 4: $\sqrt{\frac{1-\sin A}{\cos A}}$

Question : In $\triangle ABC, \angle B=90^{\circ}$ and AB : BC = 1 : 2. The value of $\cos A+\tan C$ is:

Option 1: $\frac{5+\sqrt{5}}{2 \sqrt{5}}$

Option 2: $\frac{1+\sqrt{5}}{2 \sqrt{5}}$

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

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

Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?

Option 1: $\frac{3\sqrt{3}}{5}$

Option 2: $\frac{3\sqrt{15}}{5}$

Option 3: $\frac{3\sqrt{15}}{8}$

Option 4: $\frac{3\sqrt{5}}{8}$

Question : If $\sin A=\frac{2}{3}$, then find the value of (7 – tan A)(3 + cos A).

Option 1: $\frac{61}{3}+\frac{17}{3 \sqrt{5}}$

Option 2: $\frac{61}{3 \sqrt{5}}+\frac{17}{3}$

Option 3: $\frac{61}{3}+\frac{17}{\sqrt{5}}$

Option 4: $\frac{61}{3}-\frac{17}{3 \sqrt{5}}$

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: $\frac{5}{3 \sqrt{3}}$