Question : Simplify.
$\frac{\sin8\theta \cos\theta - \sin6\theta \cos3\theta}{\cos2\theta \cos\theta - \sin3\theta \sin4\theta}$

Option 1: $\cot \theta$

Option 2: $\cot 2 \theta$

Option 3: $\tan \theta$

Option 4: $\tan 2 \theta$

Question : Simplify $\frac{\cos ^4 \theta-\sin ^4 \theta}{\sin ^2 \theta}$.

Option 1: $1-\tan ^2 \theta$

Option 2: $\tan ^2 \theta-1$

Option 3: $\cot ^2 \theta-1$

Option 4: $1-\cot ^2 \theta$

Question : If $\sin^2\theta = \cos^3\theta$, then the value of $(\cot^2\theta -\cot^6\theta)$ is:

Option 1: –1

Option 2: 0

Option 3: 2

Option 4: 1

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 : 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: $\tan \theta$