Question 78
Given that $x$ is a positive real, find the maximum possible value of
$$
\sin \left(\tan^{-1}\left(\frac{x}{9}\right)-\tan^{-1}\left(\frac{x}{16}\right)\right)
$$
$$
\sin \left(\tan^{-1}\left(\frac{x}{9}\right)-\tan^{-1}\left(\frac{x}{16}\right)\right)
$$