If sinA = 513 and 7cotB = 24, then the value of (secAcosB)(cosecBtanA) is:

Answer: Option C

$$\begin{array}{rl}& \sin A=\frac{5}{13}=\frac{P}{H};B=12\\ & \left[5,12,13\text{are triplet}\right]\\ & 7\cot B=24\\ & \cot B=\frac{24}{7}=\frac{B}{P};H=25\\ & \left[7,24,25\text{are triplet}\right]\\ & \Rightarrow \left(\sec A\cos B\right)\left(\text{cosec}B\tan A\right)\\ & =\left(\frac{13}{12}\times \frac{24}{25}\right)\left(\frac{25}{7}\times \frac{5}{12}\right)\\ & =\frac{26}{25}\times \left(\frac{25}{7}\times \frac{5}{12}\right)\\ & =\frac{65}{42}\end{array}$$