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 : 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 : If $\cot 3 \mathrm{~A}=\tan \left(\mathrm{A}-36^{\circ}\right)$, then what is the value of $\mathrm{A}$?

Option 1: 33.5 degrees

Option 2: 25 degrees

Option 3: 30 degrees

Option 4: 31.5 degrees

Question : Simplify the given equation: $\frac{\cot^3A–1}{\cot A–1}$

Option 1: $\operatorname{cosec}^2 \mathrm{A}-\cot \mathrm{A}$

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

Option 3: $\cot ^2 \mathrm{A}+\operatorname{cosec} \mathrm{A}$

Option 4: $\cot ^2 \mathrm{A}-\operatorname{cosec} \mathrm{A}$

Question : The value of $\left(\operatorname{cosec}^2 B-1\right)\left(\sec ^2 B-1\right)$ is:

Option 1: 4

Option 2: 3

Option 3: 2

Option 4: 1