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: $\frac{1}{3}$

Question : If $\cos ^2 \theta-\sin ^2 \theta=\tan ^2 \phi$, then which of the following is true?

Option 1: $\cos \theta \cos \phi=1$

Option 2: $\cos ^2 \phi-\sin ^2 \phi=\tan ^2 \theta$

Option 3: $\cos ^2 \phi-\sin ^2 \phi=\cot ^2 \theta$

Option 4: $\cos \theta \cos \phi=\sqrt{2}$

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 : 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: $\tan \theta$

Question : If $\theta$ is an acute angle and $\sin \theta+\operatorname{cosec} \theta=2$, then the value of $\sin ^5 \theta+\operatorname{cosec}^5 \theta$ is:

Option 1: 10

Option 2: 2

Option 3: 4

Option 4: 5