Let ABC be a triangle right angled at C, then what is \tan A+\tan B equal to?
- A. \frac{a}{bc}
- B. \frac{a^2}{bc}
- C. \frac{b^2}{ca}
- D. \frac{c^2}{ab} ✓
Correct Answer: D. \frac{c^2}{ab}
Explanation
In \Delta ABC with \angle C = 90^\circ, \tan A = \frac{a}{b} and \tan B = \frac{b}{a}. Summing them gives \frac{a}{b} + \frac{b}{a} = \frac{a^2+b^2}{ab}. Since a^2+b^2=c^2 (Pythagoras theorem), it evaluates to \frac{c^2}{ab}.
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