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 : 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 : What is the value of $\frac{\sin (A+B)}{\sin A \cos B}$?

Option 1: $1 + \cot A \tan B$

Option 2: $1 + \tan A \cot B$

Option 3: $1 – \sin A \cos B$

Option 4: $1 − \cot A \tan B$

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 : If $A+B=90^{\circ}$, then the expression $\frac{\cot A}{\cot B}+\cos ^2 A+\cos ^2 B$ is equal to:

Option 1: $\cot ^2 B$

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

Option 3: $\cot ^2 A$

Option 4: $\operatorname{cosec}^2 B$