Question

If tan A = ã and tan B=16calculate and simplify the following:?tan(A - B) = +

Answer 1

`\begin{gathered} In\text{ Trigonometry} \\ \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\text{ tan B}}_{} \end{gathered}`

Given:

`\begin{gathered} \tan \text{ A= }(5)/(6) \\ \tan \text{ B= }(1)/(6) \end{gathered}`

Now substitute these given into the expression above:

`\tan (A-B)=((5)/(6)-(1)/(6))/(1+((5)/(6)*(1)/(6)))`

Simplifying further:

`=((2)/(3))/(1+(5)/(36))`
`\begin{gathered} =((2)/(3))/((41)/(36)) \\ =(2)/(3)*(36)/(41) \\ =(72)/(123) \\ =(24)/(41) \end{gathered}`

The answer therefore is:

`(24)/(41)`