Question : What is the value of $\sqrt{\frac{\operatorname{cosec} A+1}{\operatorname{cosec} A-1}}+\sqrt{\frac{\operatorname{cosec} A-1}{\operatorname{cosec} A+1}}$?

Option 1: $2 \cos A$

Option 2: $\sec A$

Option 3: $2\cos A$

Option 4: $2 \sec A$

Question : What is the value of $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$?

Option 1: $2 \sec \theta$

Option 2: $2 \operatorname{cosec} \theta$

Option 3: $2 \cot \theta$

Option 4: $\operatorname{cosec} \theta+\cot \theta$

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

Option 1: $2 \sec A$

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

Option 3: $ \sec A$

Option 4: $ \operatorname{cosec} A$

Question : What is the value of $\frac{1+\tan A}{\operatorname{cosec} A}+\frac{1+\cot A}{\sec A}$?

Option 1: $2\sec^2A$

Option 2: $\sec \mathrm{A} - \mathrm{cosec A}$

Option 3: $\sec \mathrm{A} + \mathrm{cosec A}$

Option 4: $2 \;\mathrm{cosec^2 A}$

Question : The given expression is equal to:
$\frac{\left(1+\tan^2 A\right)}{\operatorname{cosec}^2 A \cdot \tan A}$

Option 1: $\sec^2A$

Option 2: $\sec A$

Option 3: $\tan A$

Option 4: $\tan^2A$