Question : Simplify the following expression: $\frac{1-\sin A}{\cos A}+\frac{\cos A}{1-\sin A}$

Option 1: $2 \cos A$

Option 2: $2 \tan A$

Option 3: $2 \sec A$

Option 4: $2 \sin A$

Question : The given expression is equal to $\frac{\sin^4 A+\cos^4 A}{1-2 \sin^2 A \cos^2 A}$:

Option 1: 1

Option 2: –1

Option 3: 0

Option 4: 2

Question : Simplify the given expression: $\frac{\sin^2 32^{\circ}+\sin^2 58^{\circ}}{\cos^2 32^{\circ}+\cos^2 58^{\circ}}+\sin^2 53^{\circ}+\cos 53^{\circ} \sin 37^{\circ}$

Option 1: 2

Option 2: –1

Option 3: –2

Option 4: 1

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 : If $\sin \theta+\cos \theta=\frac{1}{29}$, then find the value of $\frac{\operatorname{sin} \theta+\operatorname{cos} \theta}{\operatorname{sin} \theta-\operatorname{cos} \theta}$.

Option 1: $\frac{1}{41}$

Option 2: $\frac{43}{29}$

Option 3: $\frac{41}{29}$

Option 4: $\frac{1}{43}$