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 : If $x\cos^{2}30^{\circ}\cdot \sin60^{\circ}=\frac{\tan^{2}45^{\circ}\cdot \sec60^{\circ}}{\operatorname{cosec}60^{\circ}}$, then the value of $x$ is:

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

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

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

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

Question : Find the value of the given expression.
$\frac{4}{3} \tan^2 45^{\circ}+3 \cos^2 30^{\circ}-2 \sec^2 30^{\circ}-\frac{3}{4} \cot^2 60^{\circ}$

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

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

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

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

Question : What is the value of $\sin 30^{\circ}+\cos 30^{\circ}+\tan 30^{\circ}$?

Option 1: $\frac{5+\sqrt{3}}{2 \sqrt{3}}$

Option 2: $\frac{5-\sqrt{3}}{2 \sqrt{3}}$

Option 3: $\frac{5+\sqrt{3}}{\sqrt{3}}$

Option 4: $\frac{5-\sqrt{3}}{\sqrt{3}}$

Question : What is the value of $\sin 75^{\circ}+\sin 15^{\circ}$?

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

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

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

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