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 $\sin \theta+\cos \theta=\frac{\sqrt{11}}{3}$, 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: $\frac{\sqrt{7}}{3}$

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 $\cos \theta+\sec \theta=2$, then the value of $\sin ^6 \theta+\cos ^6 \theta$ is:

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

Option 2: $0$

Option 3: $1$

Option 4: $\frac{1}{2}$

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: $\frac{1}{3}$