Question : If $\sin\theta+\cos\theta=\sqrt{2}\cos\theta$, then the value of $\cot\theta$ is:

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

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

Option 3: $\sqrt{3}-1$

Option 4: $\sqrt{3}+1$

Question : The value of $\frac{\sin\theta-2\sin^{3}\theta}{2\cos^{3}\theta-\cos\theta}$ is equal to:

Option 1: $\sin\theta$

Option 2: $\cos\theta$

Option 3: $\tan\theta$

Option 4: $\cot\theta$

Question : If $6 \cot \theta=5$, then find the value of $\frac{(6 \cos \theta+\sin \theta)}{(6 \cos\theta-4 \sin\theta)}$

Option 1: 5

Option 2: 1

Option 3: 6

Option 4: 0

Question : If $\tan \theta+\sin \theta=A$ and $\tan \theta-\sin \theta=B$, then what is the value of $A^2-B^2$?

Option 1: $\tan \theta \sin \theta$

Option 2: $4 \cot \theta$

Option 3: $4 \tan \theta \sin \theta$

Option 4: $2 \tan \theta \sin \theta$

Question : If $(\sin \theta-\cos \theta)=0$, then the value of $\sin\;(\pi-\theta)+\sin \left(\frac{\pi}{2}-\theta\right)$ is:

Option 1: $1$

Option 2: $0$

Option 3: $\sqrt{3}$

Option 4: $\sqrt{2}$