Question

If tan A =5/6 and tan B = 1/6calculate and simplify the following:tan(A + B) =

Answer 1

It is given that tanA = 5/6 and tan B = 1/6

We need to solve for the tan(A+B)

From the expression of trigometric ratio for the tan(A+B).

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$

Substitute the value of tan A =5/6 and tan B = 1/6 in the expression.

$\begin{gathered} \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B} \\ \tan (A+B)=\frac{\frac{5}{6}+\frac{1}{6}}{1-\frac{5}{6}\times\frac{1}{6}} \\ \tan (A+B)=\frac{\frac{6}{6}}{1-\frac{5}{36}} \\ \tan (A+B)=\frac{1}{\frac{36-5}{36}} \\ \tan (A+B)=\frac{1}{\frac{31}{36}} \\ \tan (A+B)=\frac{36}{31} \end{gathered}$

Answer: tan(A+B) = 36/31