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)=(\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)=(\tan A+\tan B)/(1-\tan A\tan B) \\ \tan (A+B)=((5)/(6)+(1)/(6))/(1-(5)/(6)*(1)/(6)) \\ \tan (A+B)=((6)/(6))/(1-(5)/(36)) \\ \tan (A+B)=(1)/((36-5)/(36)) \\ \tan (A+B)=(1)/((31)/(36)) \\ \tan (A+B)=(36)/(31) \end{gathered}`

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