Question

If tanA = -1/2 and tanB = -1/3, then A+B can be

Answer 1

tan( A + B ) = tanA + tanB  /  1 -  tanA*tanB =  -5/6  / 1 -  1/6 =  -1

hence   A + B = 135 degrees

Answer 2

$\text{Remember!} \\\ (\text{tan~A+tan~B})=\frac{\text{tan~A+tan~B}}{\text{1-tan~A.tan~B}} \\\\ ~~~~~~~~~~~~~~~~~~~~~= \frac{ -\frac{1}{2}- \frac{1}{3} }{1-(- \frac{1}{2} . -\frac{1}{3} )} \\\\ ~~~~~~~~~~~~~~~~~~~~~= \frac{\frac{-3-2}{6} }{1-( \frac{1}{6} )} \\\\ ~~~~~~~~~~~~~~~~~~~~~= \frac{ \frac{-5}{6} }{ \frac{6-1}{6} } \Rightarrow \text{Strikerough~6} \\\\ ~~~~~~~~~~~~~~~~~~~~~= \frac{-5}{5} \\\\ ~~~~~~~~~~~~~~~~~~~~~=-1$

Therefore 
arctan(-1)=-45° ⇔180-45=135°
or =3π 
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