Which one of the following is correct ?
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. p - q = 0
- B. 2pq - 1 = 0 ✓
- C. pq - 2 = 0
- D. pq - 1 = 0
Correct Answer: B. 2pq - 1 = 0
Explanation
Let \theta = 90^\circ. Then \sin 90^\circ = 1 and \cos 90^\circ = 0. Substituting these values gives p = \frac{1}{1+0+1} = \frac{1}{2} and q = \frac{1+1}{1+1-0} = 1. The product pq = \frac{1}{2} \times 1 = \frac{1}{2}. Thus, 2pq = 1, which means 2pq - 1 = 0.
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