Question

For any right angled triangle $ABC,$ right angled at $\angle C.$
Then value of $\tan A+\tan B.$
(Where $a,b,c$ are the side lengths opposite to angles $A,B,C$ respectively)

• A. $\frac{c^2}{ab}$
• B. $\frac{c^2}{a}$
• C. $\frac{c^2}{b}$
• D. $\frac{c^2}{2ab}$

Answer 1

The correct option is A $\frac{c^2}{ab}$

Given a right angled triangle $ABC,$ right angled at $C$ with side lengths $a,b,c$ as shown:


Now, for $\Delta ABC$
$\tan A+\tan B=\frac{a}{b}+\frac{b}{a}$

$\Rightarrow \tan A+\tan B=\frac{a^2+b^2}{ab}$

$\because \Delta ABC$ is a right - angled triangle
$\Rightarrow a^2+b^2=c^2$
$\Rightarrow \tan A+\tan B=\frac{a^2+b^2}{ab}=\frac{c^2}{ab}$