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 : The value of $\frac{2 \cos ^3 \theta-\cos \theta}{\sin \theta-2 \sin ^3 \theta}$ is:

Option 1: $\sec \theta$

Option 2: $\sin \theta$

Option 3: $\cot \theta$

Option 4: $\tan \theta$

Question : The value of $(\operatorname{cosec}A+\cot A)(1 - \cos A)$ is:

Option 1: $\cos A$

Option 2: $\tan A$

Option 3: $\cot A$

Option 4: $\sin A$

Question : Simplify $\frac{\cos ^4 \theta-\sin ^4 \theta}{\sin ^2 \theta}$.

Option 1: $1-\tan ^2 \theta$

Option 2: $\tan ^2 \theta-1$

Option 3: $\cot ^2 \theta-1$

Option 4: $1-\cot ^2 \theta$