Question

If the median $AD$ of triangle $ABC$ is perpendicular to $AB$, then $p\tan A+q\tan B=0$. Find $p+q$.

Answer 1

$\theta =90°+B$

$(1+1)\cot (B+90°)=\cot 90°-\cot (A-90°)$

$-2\tan B=\tan A$

$\tan A+2\tan B=0$

$P=1,q=2$

$P+q=1+2=3$

Hence, $3$ is the correct answer.