Question : The value of $\frac{1+\sin A}{\cos A}+\frac{\cos A}{1+\sin A}$ is:

Option 1: $2 \sec A$

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

Option 3: $ \sec A$

Option 4: $ \operatorname{cosec} A$

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 : What is the value of the expression: $\sin A(1+\frac{\sin A}{\cos A})+\cos A(1+\frac{\cos A}{\sin A})$?

Option 1: $\sec A+\operatorname{cosec}A$

Option 2: $\sin \mathrm{A}+\cos \mathrm{A}$

Option 3: $\sin \mathrm{A}-\cos \mathrm{A}$

Option 4: $\sec \mathrm{A}-\operatorname{cosec} \mathrm{A}$

Question : The value of $\frac{\operatorname{sin} 58^{\circ}}{\cos 32^{\circ}}+\frac{\sin 55^{\circ} \sec 35^{\circ}}{\tan 5^{\circ} \tan 45^{\circ} \tan 85^{\circ}}$ is equal to:

Option 1: 2

Option 2: 1

Option 3: 0

Option 4: 3

Question : If $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$, then the value of $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2 \theta}$ is:

Option 1: $\frac{16}{25}$

Option 2: $\frac{40}{41}$

Option 3: $\frac{41}{40}$

Option 4: $\frac{31}{30}$