Question

If $\triangle ABC$ is right-angled at $C$, then the value of $\tan A + \tan B$ is:

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

Answer 1

The Correct Option is C

In a right triangle, $\tan A = \frac{BC}{AC}$ and $\tan B = \frac{AC}{BC}$.
Then: $\tan A + \tan B = \frac{BC}{AC} + \frac{AC}{BC} = \frac{BC^2 + AC^2}{BC \cdot AC}$. 
Using the Pythagorean theorem, $BC^2 + AC^2 = AB^2 = c^2$. 
Hence: $\tan A + \tan B = \frac{c^2}{ab}$.