Question

In a triangle $ABC$, right angled at $C$, find the value of $\tan A+\tan B$ in terms of the sides $a,b,c$.

Answer 1

$\tan A=\frac{a}{b}\tan B=\frac{b}{a}$
$\therefore \tan A+\tan B=\frac{a}{b}+\frac{b}{a}$
$=\frac{a^2+b^2}{ab}$
$=\frac{c^2}{ab}(\because c^2=a^2+b^2)$