Question : If $\sin A=\frac{5}{13}$ and $7 \cot B=24$, then the value of $(\sec A \cos B)(\operatorname{cosec} B \tan A)$ is:

Option 1: $\frac{65}{42}$

Option 2: $\frac{13}{14}$

Option 3: $\frac{15}{13}$

Option 4: $\frac{13}{7}$

Question : If $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}=\frac{3}{2}$, then the value of $\sin ^4 \theta-\cos ^4 \theta$ is:

Option 1: $\frac{5}{12}$

Option 2: $\frac{12}{13}$

Option 3: $\frac{11}{12}$

Option 4: $\frac{5}{13}$

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: $\operatorname{cosec} \theta$

Question : If $\cot A=\frac{12}{5}$, then the value of $\sin A=?$

Option 1: $\frac{5}{13}$

Option 2: $\frac{12}{13}$

Option 3: $\frac{5}{12}$

Option 4: $\frac{13}{12}$

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: $\cot \theta$