Question

$\triangle A B C$ is right angled at $C$, then $\tan A+\tan B$ is equal to

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

Answer 1

Answer: (D)

$\tan A=\frac{a}{b}, \tan B=\frac{b}{a}$
$\therefore \tan A+\tan B=\frac{a^2+b^2}{a b}$
Since, $ a^2+b^2=c^2$
$\therefore \tan A+\tan B=\frac{c^2}{a b}$