Question : $\sqrt{\frac{1+\sin A}{1-\sin A}}=$_______.

Option 1: $\operatorname{coesc} A-\cot A$

Option 2: $\sec A-\tan A$

Option 3: $\sec A+\tan A$

Option 4: $\sec A$

Question : $\frac{(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)}{(\sec \theta+\tan \theta)(1-\sin \theta)}$ is equal to:

Option 1: $2 \sec \theta$

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

Option 3: $\operatorname{cosec} \theta$

Option 4: $\sec \theta$

Question : The value of $\sqrt{\frac{1+\cos A}{1-\cos A}}$ 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 : For any real values of $\theta, \sqrt{\frac{\sec\theta \:-\: 1}{\sec\theta \:+\: 1}}=$?

Option 1: $\cot\theta - \operatorname{cosec}\theta$

Option 2: $\sec\theta - \tan\theta$

Option 3: $\operatorname{cosec}\theta - \cot\theta$

Option 4: $\tan\theta - \sec\theta$

Question : The value of $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}$ is:

Option 1: $\sec\theta+\tan \theta$

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

Option 3: $\operatorname{cosec} \theta+\cot \theta$

Option 4: $\sec\theta-\tan \theta$

Question : $\frac{\sec A(\sec A+\tan A)(1-\sin A)}{\left(\operatorname{cosec}^2 A-1\right) \sin ^2 A}$ is equal to:

Option 1: $\cot A$

Option 2: $\cos A$

Option 3: $\sec ^2 A$

Option 4: $\cos ^2 A$