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 $\cos \theta+\cos ^2 \theta=1$, find the value of $\sqrt{\sin ^4 \theta+\cos ^2 \theta}$.

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

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

Option 3: $\sqrt{2} \operatorname{sin} \theta$

Option 4: $2 \operatorname{sin} \theta$

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

Option 1: 2

Option 2: 4

Option 3: 0

Option 4: 1

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 : For any acute angle $\theta, \sin \theta+\sin^2 \theta=1$, then the value of $\cos^2 \theta+\cos^4 \theta=$___________.

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1