tan A = 2/3 and tan b= -3/5 . what exact value of cot (A-B)

tan A = 2/3 and tan b= -3/5 . what exact value of cot (A-B)

$$\small{\text{$ \boxed{~\cot{(A-B)} =\dfrac{ 1+\tan{(A)} \cdot \tan{(B)} }{ \tan{(A)} - \tan{(B)} } ~} $}}$$

$$\small{\text{$ \begin{array}{lcl} \cot{(A-B)} &=&\dfrac { 1+\dfrac23 \cdot \left(\dfrac{-3}{5}\right) } { \dfrac23 - \left(\dfrac{-3}{5}\right)}\\\\ \cot{(A-B)} &=&\dfrac { 1-\dfrac23 \cdot \left(\dfrac{3}{5}\right) } { \dfrac23 + \dfrac35 }\\\\ \cot{(A-B)} &=&\dfrac { 1-\dfrac25 } { \dfrac23 + \dfrac35 }\\\\ \cot{(A-B)} &=&\dfrac { \dfrac35 } { \dfrac23 + \dfrac35 }\\\\ \cot{(A-B)} &=&\dfrac { \dfrac35 } { \dfrac{19}{15} }\\\\ \cot{(A-B)} &=& \left(\dfrac35 \right) \cdot \left(\dfrac{15}{19}\right)\\\\ \mathbf{\cot{(A-B)}} & \mathbf{=} & \mathbf{\dfrac{9}{19}} \\\\ \end{array} $}}\\\\$$

tan A=2/3, tan B=-3/5 

A=33.69, B=30.96

So the value of cot 2.73 is 20.97158

Nice work Heureka :))