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 : The given expression is equal to:
$1-\frac{\tan ^2 \phi}{\sec ^2 \phi}$

Option 1: $\operatorname{sin}^2 \phi\cos ^2 \phi$

Option 2: $\operatorname{sin}^2 \phi\cot ^2 \phi$

Option 3: $\cot^2 \phi \cos^2 \phi$

Option 4: $\tan^2 \phi\cos^2 \phi$

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 : 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 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: $\tan^2A$