Question : Possible measures of the three angles of a triangle are:

Option 1: 33°, 42°, and 115°

Option 2: 40°, 70°, and 80°

Option 3: 30°, 60°, and 100°

Option 4: 50°, 60°, and 70°

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 $\tan (A+B)=\sqrt{3}$ and $\tan (A-B)=\frac{1}{\sqrt{3}}; 0°<(A+B)<90°; A > B$, then the values of $A$ and $B$ are respectively:

Option 1: 45° and 15°

Option 2: 15° and 45°

Option 3: 30° and 30°

Option 4: 60° and 30°

Question : If $\theta>0$ be an acute angle, then the value of $\theta$ in degrees satisfying $\frac{\cos^2\theta-3 \cos\theta+2}{\sin^2\theta}=1$ is:

Option 1: 90°

Option 2: 30°

Option 3: 45°

Option 4: 60°

Question : If $\tan \frac{A}{2}=x$, then find $x$.

Option 1: $\frac{\sqrt{1+\cos A}}{\sqrt{1-\cos A}}$

Option 2: $\frac{\sqrt{1-\sin A}}{\sqrt{1+\cos A}}$

Option 3: $\frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$

Option 4: $\frac{\sqrt{\cos A-1}}{\sqrt{1+\cos A}}$