Explanation

(b)
Since, $\sin^{- 1}{\left( \frac{x}{5} \right) + cosec^{- 1}\left( \frac{5}{4} \right) = \frac{\pi}{2}}$
$\Rightarrow \ \ \sin^{- 1}{\left( \frac{x}{5} \right) + \sin^{- 1}{\left( \frac{4}{5} \right) = \frac{\pi}{2}}}$
$\Rightarrow \ \sin^{- 1}{\left( \frac{x}{5} \right) = \cos^{- 1}\left( \frac{4}{5} \right)}$
$\Rightarrow \ \sin^{- 1}{\left( \frac{x}{5} \right) = \sin^{- 1}\left( \frac{3}{5} \right)}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 3$