If $ an A = \dfrac{1}{2}$ and $ an B = \dfrac{1}{3}$, find the value of $ an(A + B)$.

Question

If $	an A = \dfrac{1}{2}$ and $	an B = \dfrac{1}{3}$, find the value of $	an(A + B)$.

Accepted Answer

$1$. $	an(A+B) = \dfrac{	an A + 	an B}{1 - 	an A	an B} = \dfrac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{6}} = \dfrac{\frac{5}{6}}{\frac{5}{6}} = 1$. Adding the tangents without dividing gives $\dfrac{5}{6}$, and using a plus sign in the denominator gives $\dfrac{5}{7}$.

Answer

A) $\dfrac{5}{6}$

Answer

B) $\dfrac{5}{7}$

Answer

C) $1$

Answer

D) $\dfrac{1}{6}$

If $\tan A = \dfrac{1}{2}$ and $\tan B = \dfrac{1}{3}$, find the value of $\tan(A + B)$.

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