Trigonometry problem#2

$\begin{aligned} \cos X=\frac { 4 }{ 5 } \Rightarrow \sin X=\frac { 3 }{ 5 } \Rightarrow \tan X=\frac { 3 }{ 4 } & & \small \color{#3D99F6} \text{ since } \sin X=\sqrt { 1-\cos ^{ 2 }{ X } } \text{ and } \tan X=\frac { \sin X }{ \cos X } \\ \sin Y=\frac { 12 }{ 13 } \Rightarrow \cos Y=\frac { 5 }{ 13 } \Rightarrow \tan Y=\frac { 12 }{ 5 } & & \small \color{#3D99F6} \text{ since } \cos Y=\sqrt { 1-\sin^{ 2 }{ Y } } \text{ and } \tan Y=\frac { \sin Y }{ \cos Y } \end{aligned} \\ \frac { \tan Y-\tan X }{ 1+\tan Y\times \tan X } =\frac { \frac { 12 }{ 5 } -\frac { 3 }{ 4 } }{ 1+\frac { 12 }{ 5 } \times \frac { 3 }{ 4 } } =\frac { 33 }{ 56 } \\ a-b=33-56=-23$