Question : If $\sin \theta-\cos \theta=0$, then find the value of $\left(\sin^3 \theta-\cos^3 \theta\right)$.

Option 1: $0$

Option 2: $2$

Option 3: $1$

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

Question : If $\frac{(3 \sin \theta-\cos \theta)}{(\cos \theta+\sin \theta)}=1$, then the value of $\cot \theta$ is:

Option 1: 3

Option 2: 0

Option 3: 1

Option 4: 2

Question : If $2 \sin \theta+2 \sin ^2 \theta=2$, then the value of $2 \cos ^4 \theta+2 \cos ^2 \theta$ is:

Option 1: 4

Option 2: 2

Option 3: 1

Option 4: 0

Question : If $\sin \theta+\sin ^2 \theta=1$, then the value of $\cos ^2 \theta+\cos ^4 \theta$ is equal to:

Option 1: 5

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

Option 3: $1$

Option 4: $0$

Question : If $x\sin^{3}\theta +y\cos^{3}\theta=\sin\theta\cos\theta$ and $x\sin\theta-y\cos\theta=0$, then the value of $\left ( x^{2}+y^{2} \right )$ equals:

Option 1: $1$

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

Option 3: $\frac{3}2$

Option 4: $2$