SOLUTION
[tex]\begin{gathered} In\text{ Trigonometry} \\ \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\text{ tan B}}_{} \end{gathered}[/tex]
Given:
[tex]\begin{gathered} \tan \text{ A= }\frac{5}{6} \\ \tan \text{ B= }\frac{1}{6} \end{gathered}[/tex]
Now substitute these given into the expression above:
[tex]\tan (A-B)=\frac{\frac{5}{6}-\frac{1}{6}}{1+(\frac{5}{6}\times\frac{1}{6})}[/tex]
Simplifying further:
[tex]=\frac{\frac{2}{3}}{1+\frac{5}{36}}[/tex][tex]\begin{gathered} =\frac{\frac{2}{3}}{\frac{41}{36}} \\ =\frac{2}{3}\times\frac{36}{41} \\ =\frac{72}{123} \\ =\frac{24}{41} \end{gathered}[/tex]
The answer therefore is:
[tex]\frac{24}{41}[/tex]
