If \( \alpha \) and \( \beta \) are complementary angles such that \( \alpha - \beta = \frac{\pi}{6} \) and \( m \tan \beta = n \tan \alpha \), then what is \( \left( \frac{m+n}{m-n} \right) \) equal to ?
- A. 2 ✓
- B. \frac{2}{\sqrt{3}}
- C. 1
- D. \frac{1}{\sqrt{3}}
Correct Answer: A. 2
Explanation
From the given equations, \alpha = 60^\circ and \beta = 30^\circ. Therefore, m \tan 30^\circ = n \tan 60^\circ, making m/n = 3. Using composendo and dividendo, (m+n)/(m-n) = (3+1)/(3-1) = 2.