Question

If angle $C$ of $△$ $ABC$ is ${90}^{\circ }$, then $\tan A+\tan B=...........$(where $a,b,c$ are sides opposite to angles A, B, C respectively)

• A. $\frac{c^2}{ab}$
• B. $\frac{a^2}{bc}$
• C. $\frac{b^2}{ac}$
• D. $\frac{c^3}{ab}$

Answer 1

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

According to the figure,

In $△ABC,\angle C={90}^{\circ }$.

By Pythagoras theorem,

We can say that,

$c^2=a^2+b^2$

Also,

$\tan A=\frac{a}{b}$ and $\tan B=\frac{b}{a}$

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