Question : Find the value of $\frac{\cos^2 15^{\circ}-\sin^2 15^{\circ}}{\cos^2 145^{\circ}+\sin^2 145^{\circ}}$.

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

Option 2: $\frac{1}{1-\sqrt{3}}$

Option 3: $\frac{\sqrt{3}}{2}$

Option 4: $\frac{2}{\sqrt{3}}$

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 $\sin(\theta+30^{\circ})=\frac{3}{\sqrt{12}}$, then the value of $\cos^{2}\theta$ is:

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

Option 2: $\frac{\sqrt{3}}{2}$

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

Option 4: $\frac{1}{2}$

Question : If $7\sin^{2}\theta+3\cos^{2}\theta=4$, and $0^{\circ}< \theta< 90^{\circ}$, then the value of $\tan\theta$ is:

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

Option 2: $\frac{1}{\sqrt{3}}$

Option 3: $\sqrt{\frac{3}{2}}$

Option 4: $1$

Question : If $x\sin^{3}\theta +y\cos^{3}\theta=\sin\theta\cos\theta$ and $x\sin\theta-y\cos\theta=0$, then the value of $\left ( x^{2}+y^{2} \right )$ equals:

Option 1: $1$

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

Option 3: $\frac{3}2$

Option 4: $2$