Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?

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

Option 2: $\sqrt{3}$

Option 3: $1$

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

Question : If $\left(\frac{\cos A}{1-\sin A}\right)+\left(\frac{\cos A}{1+\sin A}\right)=4$, then what will be the value of $A$? $\left(0^{\circ}<\theta<90^{\circ}\right)$

Option 1: $90^{\circ}$

Option 2: $45^{\circ}$

Option 3: $60^{\circ}$

Option 4: $30^{\circ}$

Question : Evaluate the following:
$\cos \left(36^{\circ}+A\right) \cdot \cos \left(36^{\circ}-A\right)+\cos \left(54^{\circ}+A\right) \cdot \cos \left(54^{\circ}-A\right)$

Option 1: $\sin 2A$

Option 2: $\cos A$

Option 3: $\sin A$

Option 4: $\cos 2A$

Question : The value of $\theta$ $ \left ( 0\leq \theta \leq 90^{\circ} \right )$ satisfying $2\sin^{2}\theta = 3\cos \theta$ is:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $90^{\circ}$

Option 4: $45^{\circ}$

Question : If $\sin\left ( 2a+45^{\circ} \right )=\cos\left ( 30^{\circ}-a \right )$ where $0^{\circ}< a< 90^{\circ}$, then the value of a is:

Option 1: $0^{\circ}$

Option 2: $15^{\circ}$

Option 3: $45^{\circ}$

Option 4: $60^{\circ}$