Question : Find the value of: $\sqrt{\frac{1 - \sin 3 \theta}{1 + \sin 3 \theta}}$

Option 1: $\sec 3 \theta - \tan 3 \theta$

Option 2: $(\sec 3 \theta - \tan 3 \theta)^3$

Option 3: $(\sec 3 \theta - \tan 3 \theta)^2$

Option 4: $\sec 3 \theta + \tan 3 \theta$

Question : Simplify the following.
$\frac{\sin^3 \alpha+\cos^3 \alpha}{\sin \alpha+\cos \alpha}$

Option 1: $1+\sin \alpha \cos \alpha$

Option 2: $\tan \alpha$

Option 3: $1-\sin \alpha \cos \alpha$

Option 4: $\sec \alpha$

Question : If $\sec A=\frac{5}{4}$, then the value of $\frac{\tan A}{1+\tan ^2 A}-\frac{\sin A}{\sec A}$ is:

Option 1: 2

Option 2: 1

Option 3: 0

Option 4: 3

Question : Simplify the following expression.
$\frac{\sin \theta - 2 \sin ^3 \theta}{2 \cos ^3 \theta - \cos \theta}$

Option 1: $\tan \theta$

Option 2: $\sin \theta$

Option 3: $\sec \theta$

Option 4: $\cos \theta$

Question : Which of the following is equal to $[\frac{\tan \theta+\sec \theta–1}{\tan \theta–\sec \theta+1}]$?

Option 1: $\frac{1+\sin \theta}{\cos \theta}$

Option 2: $\frac{1+\tan \theta}{\cot \theta}$

Option 3: $\frac{1+\cot \theta}{\tan \theta}$

Option 4: $\frac{1+\cos \theta}{\sin \theta}$