How many values does (y-x) have?
For the following two (02) items: Let \cos(2x+3y) = \frac{1}{2} and \cos(3x+2y) = \frac{\sqrt{3}}{2}, where -\pi \lt (2x+3y) \lt \pi and -\pi \lt (3x+2y) \lt \pi.
- A. Two
- B. Three
- C. Four ✓
- D. More than four
Correct Answer: C. Four
Explanation
Let u = 2x+3y and v = 3x+2y. Notice that u-v = -x+y = y-x. Evaluating all 2 \times 2 = 4 combinations of u-v yields 4 distinct values. Thus, y-x has 4 values.