Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}+\sec 45^{\circ} × \sin 45^{\circ}}{\sec 60^{\circ}+{\text{cosec}} 30^{\circ}}$ is:

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

Option 2: $-\frac{3}{8}$

Option 3: $\frac{3}{8}$

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

Question : Evaluate $\frac{\sin 54^{\circ}}{\cos 36^{\circ}}+\frac{\sec 46^{\circ}}{\operatorname{cosec} 44^{\circ}}$

Option 1: 0

Option 2: –1

Option 3: 2

Option 4: 1

Question : What is the value of the following in terms of trigonometric ratios?
$\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}$

Option 1: $2\operatorname{cosec A}$

Option 2: $2\operatorname{cos A}$

Option 3: $2\operatorname{sec A}$

Option 4: $2\operatorname{sin A}$

Question : Find the value of $\frac{\cos 37^{\circ}}{\sin 53^{\circ}}-\cos 47^{\circ} \operatorname{cosec} 43^{\circ}$.

Option 1: 0

Option 2: –1

Option 3: 2

Option 4: 1

Question : If $\frac{1}{\operatorname{cosec} \theta+1}+\frac{1}{\operatorname{cosec} \theta-1}=2 \sec \theta, 0^{\circ}<\theta<90^{\circ}$, then the value of $\frac{\tan \theta+2 \sec \theta}{\operatorname{cosec} \theta}$ is:

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

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

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

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