Question : If $0°<A<90°$, the value of $\frac{\tan A\ -\ \sec A\ -\ 1}{\tan A\ +\ \sec A\ +\ 1}$ is:

Option 1: $\frac{\sin A-1}{\cos A}$

Option 2: $\frac{1-\sin A}{\cos A}$

Option 3: $\frac{1-\cos A}{\sin A}$

Option 4: $\frac{\sin A+1}{\cos A}$

Question : $\left(\frac{\tan ^3 \theta}{\sec ^2 \theta}+\frac{\cot ^3 \theta}{\operatorname{cosec}^2 \theta}+2 \sin \theta \cos \theta\right) \div\left(1+\operatorname{cosec}^2 \theta+\tan ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $\operatorname{cosec} \theta \sec \theta$

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

Option 3: $\sin \theta \cos \theta$

Option 4: $\sec \theta$

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

Option 1: $1-\cos \theta$

Option 2: $1-\sin \theta$

Option 3: $\cos \theta$

Option 4: $\sin \theta$

Question : The expression $\frac{\cos ^4 \theta-\sin ^4 \theta+2 \sin ^2 \theta+3}{(\operatorname{cosec} \theta+\cot \theta+1)(\operatorname{cosec} \theta-\cot \theta+1)-2}, 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $\frac{1}{2} \sin \theta$

Option 2: $2 \sin \theta$

Option 3: $\sec \theta$

Option 4: $2\operatorname{cosec} \theta$

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: $\cot \theta$