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 : What is the value of $\frac{\sin (A+B)}{\sin A \cos B}$?

Option 1: $1 + \cot A \tan B$

Option 2: $1 + \tan A \cot B$

Option 3: $1 – \sin A \cos B$

Option 4: $1 − \cot A \tan B$

Question : If $1 + \sin^2 θ - 3\sinθ \cosθ = 0$, then the value of $\cotθ$ is:

Option 1: $0$

Option 2: $2$

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

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

Question : If $\operatorname{cos} \theta+\operatorname{sin} \theta=\sqrt{2} \operatorname{cos} \theta$, find the value of $(\cos \theta-\operatorname{sin} \theta)$

Option 1: $\sqrt{2} \sin \theta$

Option 2: $\sqrt{2} \cos \theta$

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

Option 4: $\frac{1}{2}\cos \theta$

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

Option 1: $\frac{x}{(1+x)}$

Option 2: $x$

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

Option 4: $\frac{(1+x)}{x}$