What is p^2q^2(p^2 + q^2 + 3) equal to?
For the following two (02) items: Let \operatorname{cosec} \theta - \sin \theta = p and \sec \theta - \cos \theta = q.
- A. 0
- B. 1 ✓
- C. 2
- D. 4
Correct Answer: B. 1
Explanation
Substituting \theta = 45^\circ gives p = \sqrt{2} - \frac{1}{\sqrt{2}} = \frac{1}{\sqrt{2}} and q = \frac{1}{\sqrt{2}}. Evaluating p^2q^2(p^2 + q^2 + 3) = (\frac{1}{2})(\frac{1}{2})(\frac{1}{2} + \frac{1}{2} + 3) = \frac{1}{4}(4) = 1.
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