What is (p\sin \theta + q\cos \theta) equal to?
For the following two (02) items: Let \operatorname{cosec} \theta - \sin \theta = p and \sec \theta - \cos \theta = q.
- A. -1
- B. 0
- C. 1 ✓
- D. 2
Correct Answer: C. 1
Explanation
We can simplify p = \frac{1-\sin^2 \theta}{\sin \theta} = \frac{\cos^2 \theta}{\sin \theta} and q = \frac{1-\cos^2 \theta}{\cos \theta} = \frac{\sin^2 \theta}{\cos \theta}. Then p\sin \theta + q\cos \theta = \cos^2 \theta + \sin^2 \theta = 1.
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