Question : The value of $\sqrt{\frac{1+\sin A}{1-\sin A}}$ is:

Option 1: $\sec A-\tan A$

Option 2: $\operatorname{cosec} A+\cot A$

Option 3: $\sec A+\tan A$

Option 4: $\operatorname{cosec} A-\cot A$

Question : If $\operatorname{cos} \theta+\operatorname{sin} \theta=\sqrt{2} \operatorname{cos} \theta$, find the value of $(\cos \theta-\operatorname{sin} \theta)$

Option 1: $\sqrt{2} \sin \theta$

Option 2: $\sqrt{2} \cos \theta$

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

Option 4: $\frac{1}{2}\cos \theta$

Question : The value of $\frac{\sin A}{\cot A+\operatorname{cosec} A}-\frac{\sin A}{\cot A-\operatorname{cosec} A}+1$ is:

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

Option 2: $3$

Option 3: $0$

Option 4: $2$

Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}-\sec 35^{\circ} \cdot \sin 55^{\circ}}{\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}}$ is equal to:

Option 1: $\frac{1}{8}$

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

Option 3: $\frac{1}{4}$

Option 4: $-\frac{1}{8}$

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