Question : $7 \sin ^2 A+3 \cos ^2 A=4$, then find $\cot A$:

Option 1: $\sqrt{3}$

Option 2: $\sqrt{2}$

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

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

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 : If $\frac{2 \sin A-\cos A}{\sin A+\cos A}=1$, then find the value of $\cot A$.

Option 1: $1$

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

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

Option 4: $2$

Question : If $\sin A=\frac{\sqrt{3}}{2}, 0<A<90^{\circ}$, then find the value of $2(\operatorname{cosec} A + \cot A)$.

Option 1: $2 \sqrt{3}$

Option 2: $\sqrt{3}$

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

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

Question : If $\sin \theta+\cos \theta=\frac{\sqrt{11}}{3}$, then the value of $(\cos \theta-\sin \theta)$ is:

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

Option 2: $\frac{7}{3}$

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

Option 4: $\frac{\sqrt{7}}{3}$