Question

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

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

Answer 1

Answer: (D)

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