Question : If $\cos \theta-\sin \theta=\sqrt{2} \sin \theta$, then $(\cos \theta+\sin \theta)$ is:

Option 1: $-\sqrt{2} \cos \theta$

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

Option 3: $\sqrt{2} \tan \theta$

Option 4: $-\sqrt{2} \sin \theta$

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 $\operatorname{cos} \theta+\operatorname{sin} \theta=\sqrt{2} \operatorname{cos} \theta$, 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 : 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: $1-\cot ^2 \theta$

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: $\tan \theta$