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 $\sin \theta+\cos \theta=\frac{\sqrt{11}}{3}$, then what is $\sin \theta-\cos \theta$?

Option 1: $\frac{\sqrt{7}}{4}$

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

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

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

Question : If $\sin (A-B)=\sin A \cos B–\cos A\sin B$, then $\sin 15°$ will be:

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

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

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

Option 4: $\frac{\sqrt{3}–1}{2\sqrt{2}}$

Question : If $\sin \theta+\cos \theta=\sqrt{2} \cos \theta$, then find $\frac{\sin \theta-\cos \theta}{\sin \theta}$:

Option 1: $-\sqrt{2}$

Option 2: $-1$

Option 3: $1$

Option 4: $\sqrt{2}$

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