Question : What is the value of $\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$?

Option 1: $\sqrt{3}$

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

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

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

Question : What is the value of $\cos ^2 15°?$

Option 1: $(2+\sqrt{3})$

Option 2: $\frac{(2+\sqrt{3})}{4}$

Option 3: $\frac{(2+\sqrt{3})}{2}$

Option 4: $\frac{(1+\sqrt{3})}{2}$

Question : What is the value of $\cos45° \sin15°$?

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

Option 2: $\frac{(\sqrt{3}-1)}{4}$

Option 3: $(\sqrt{3}+1)$

Option 4: $2 \sqrt{3}-1$

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 $2 \cot \theta = 3$, find the value of $\frac{\sqrt{13} \sin \theta – 3 \tan \theta}{3 \tan \theta + \sqrt{13} \cos \theta}$

Option 1: $\frac{1}{\sqrt{13}}$

Option 2: $\frac{2}{\sqrt{13}}$

Option 3: 0

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