Question : If $b \cos \theta=a$, then $\operatorname{cosec} \theta+\cot \theta=$_______.

Option 1: $\sqrt{\frac{1}{b+a}}$

Option 2: $\sqrt{\frac{b-a}{b+a}}$

Option 3: $\sqrt{\frac{b+a}{b-a}}$

Option 4: $\sqrt{\frac{1}{b-a}}$

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 : $\frac{1+\cos \theta-\sin ^2 \theta}{\sin \theta(1+\cos \theta)} \times \frac{\sqrt{\sec ^2 \theta+\operatorname{cosec}^2 \theta}}{\tan \theta+\cot \theta}, 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $\sin \theta$

Option 2: $\cos \theta$

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

Option 4: $\cot \theta$

Question : $ \sqrt{\frac{1+\cos \theta}{1-\cos \theta}}+\sqrt{\frac{1-\cos \theta}{1+\cos \theta}}=$________.

Option 1: $2 \sin \theta$

Option 2: $2 \cos \theta$

Option 3: $ 2 \operatorname{cosec} \theta $

Option 4: $2 \sec \theta$

Question : If $\operatorname{cosec} \theta+\cot \theta=2$, then what is the value of $\operatorname{cosec} \theta$?

Option 1: $\frac{5}{4}$

Option 2: $\sqrt{2}$

Option 3: $\sqrt{5}$

Option 4: $\frac{3}{2}$

Question : If $\operatorname{cosec} \theta+\cot \theta=p$, then the value of $\frac{p^2-1}{p^2+1}$ is:

Option 1: $\cos \theta$

Option 2: $\sin \theta$

Option 3: $\cot \theta$

Option 4: $\operatorname{cosec} \theta$