What is \frac{p}{q} equal to?
For the following two (02) items: Let \sin A + \sin B = p and \cos A + \cos B = q.
- A. \tan(\frac{A-B}{2})
- B. \cot(\frac{A-B}{2})
- C. \tan(\frac{A+B}{2}) ✓
- D. \cot(\frac{A+B}{2})
Correct Answer: C. \tan(\frac{A+B}{2})
Explanation
Applying sum-to-product formulas, p = 2\sin(\frac{A+B}{2})\cos(\frac{A-B}{2}) and q = 2\cos(\frac{A+B}{2})\cos(\frac{A-B}{2}). Dividing them gives \frac{p}{q} = \frac{\sin(\frac{A+B}{2})}{\cos(\frac{A+B}{2})} = \tan(\frac{A+B}{2}).