What is \left(p + \frac{1}{q}\right)\left(q + \frac{1}{p}\right) equal to ?
For the next two (02) items that follow : p = \frac{\sin \theta}{1 + \cos \theta + \sin \theta} and q = \frac{1 + \sin \theta}{1 + \sin \theta - \cos \theta}
- A. \frac{1}{2}
- B. \frac{17}{4}
- C. \frac{9}{2} ✓
- D. \frac{21}{4}
Correct Answer: C. \frac{9}{2}
Explanation
Expanding the given expression yields pq + 1 + 1 + \frac{1}{pq} = pq + \frac{1}{pq} + 2. Using the identity derived in the previous question where pq = \frac{1}{2}, substituting this value gives \frac{1}{2} + 2 + 2 = 4.5 = \frac{9}{2}.
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