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 : Find the value of $\left(\tan ^2 \theta+\tan ^4 \theta\right)$.

Option 1: $\cot ^2 \theta-\tan ^2 \theta$

Option 2: $\ {\sec}^4 \theta-\ {\sec}^2 \theta$

Option 3: $\ {\sec}^4 \theta-\ {\sec}^4 \theta$

Option 4: $ \ {\sec}^4 \theta+\ {\sec}^2 \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 $(\operatorname{cosec}A+\cot A)(1 - \cos A)$ is:

Option 1: $\cos A$

Option 2: $\tan A$

Option 3: $\cot A$

Option 4: $\sin A$

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: $1 − \cot A \tan B$