Question

If $a,b,c$ are the sides of a triangle $ABC$ opposite to angles $A,B,C$ respectively and angle $C$ is ${90}^{\circ },$ then $\tan A+\tan B$ is equal to

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

Answer 1

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

Clearly, $\Delta ACB$ is right angled triangle.


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