If angle $C$ of a triangle $A B C$ is a right angle, then what is $\tan \mathrm{A}+\tan \mathrm{B}$ equal to?

• A

  $\frac{a^2-b^2}{a b}$
• B

  $\frac{a^2}{b c}$
• C

  $\frac{b^2}{c a}$
• Correct answer
  D

  $\frac{c^2}{a b}$

Solution

we have $c^2=a^2+b^2$ $\begin{aligned} & \tan A+\tan B=\frac{a}{b}+\frac{b}{a} \\ & =\frac{a^2+b^2}{a b}=\frac{c^2}{a b} \end{aligned}$

Hence, the correct answer is option: 'D'.