Question : If $\sin 23^{\circ}=\frac{a}{b}$, the value of $\sec 23^{\circ}-\sin 67^{\circ}$ is:

Option 1: $\frac{a^2}{\sqrt{b^2-a^2}}$

Option 2: $\frac{b^2-a^2}{a b}$

Option 3: $\frac{a^2}{b\sqrt{b^2+a^2}}$

Option 4: $\frac{a^2}{b \sqrt{b^2-a^2}}$

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

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 : What will be the value of $\sin 10^{\circ}- \frac{4 }{ 3} \sin ^3 10^{\circ}?$

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

Option 2: $\frac{1}{6}$

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

Option 4: $\frac{\sqrt{3}}{6}$

Question : What is the value of $\sec^2 54^{\circ}-\cot 2 36^{\circ}+\frac{3}{2} \sin^2 37^{\circ} \times \sec^2 53^{\circ}+\frac{2}{\sqrt{3}} \tan 60^{\circ}$?

Option 1: $\frac{5}{2}$

Option 2: $\frac{9}{2}$

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

Option 4: $\frac{7}{2}$