Question

If tan A = { and tan B = 3calculate and simplify the following:?tan(A - B) = +

Answer 1

We will employ the compound angle formula;

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

We substitute the values for tanA and tanB to obtain;

$\tan (A-B)=\frac{\frac{4}{3}-\frac{3}{5}}{1-\frac{4}{3}(\frac{3}{5})}$

After rearranging and simplifying, we obtain;

$\tan (A-B)=+\frac{11}{3}$