If sinA = $$\frac{5}{{13}}$$ and 7cotB = 24, then the value of (secAcosB)(cosecBtanA) is:

Solution (By Examveda Team)

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